I don't think reliability of muslim traders and efforts of sufi scholars in the region were simple reasons for natives to convert to Islam considering the horror created by dutch and portugese expansionism, which eventually accelerated the process of spread of Islam among native folks.
This point is very controversial and scholars seem to be divided. If Malay rulers had converted to Islam in order to find allies against the Portuguese, and later Dutch, then this would explain their conversion very easily. The problem is that the dates don't work. The trading cities and power centres converted in a wave travelling from west to east: north Sumatra in the early 14th century, Malaya in the 15th century, Java in the 16th century AD. The process had started before the Europeans arrived. Although this game is called Europa Universalis, not every part of history started in Europe, as you know!
Secondly, there's no such thing as missionaries in Islamic literature as in the case of catholic faith.
As you have said, there were Sufi scholars in the region. Why were they there, in an area with few Muslims, far from the scholars of Mecca and Cairo? Some of them had been sent by their order (tariqa) specifically to spread and strengthen their faith, so they were missionaries. The most famous is Abd' al-Ra'uf Singkel of the Shattariyya. They taught the Muslim merchants how to live, which included business, which meant that they had to teach Malay rulers how to do business according to Islamic teaching. While there had been Arab traders for centuries, the Sufi scholars seem to have been a new development in the 14th century, which explains why conversions began to happen at that time.
You couldn't just send some missionaries to convert a foreign ruler immediately. That's neither logical nor possible.
That is certainly a strategy that Christian missionaries have tried many times;
Augustine of Canterbury is a famous example. And Malaysian scholars usually think that is what happened in southeast Asia. For example:
Ahmad Fauzi Abdul Hamid said:
The decisive step was almost always the conversion of a local ruler ... (p. 472)
In propagating the faith to the rajas (kings) and rulers of the Malay world, they [Sufi missionaries] did not expect a swift wholesale transformation of the state into one resembling the Prophet's Islamic state of Madinah. Instead, they calculated that the Malay masses, still imbued with the Hindu concept of dewaraja i.e. of the king being the incarnation of a deity, would follow without hesitation the example set by their leaders and hence speeding up the pace of their being brought into the fold of Islam. Proselytisation of the rulers, far from being an end in itself, served as a means towards large-scale missionary activities. (p.485)
Truth is, muslim arab merchants had very firm trade connections with the far East and India ever since the 7th century. They used to trade in China, Korea, Bengal and southeastern Asia. So they were well known by the native people. Besides, the sufi masters I mentioned above managed to familiarise the people with Islam by serving as models.
Yes, all this is true. But you seem to think that this was not a political process. I think your language could be understood as people watching a Muslim doing deals in a small bazaar, admiring their honesty, and converting. But these were not small businesspeople. Trading across the Indian Ocean needed large amounts of capital; these were the multinational corporations of the 14th and 15th centuries. And that had two effects.
Firstly, the Muslim merchants managed these complex businesses arrangements through Islamic commercial law, which was more developed than the existing systems in southeast Asia. When the sources talk about the honesty of Muslim merchants, they mean their advanced legal technology. And unlike today, there were no secular lawyers: the legal experts were those Sufi scholars. The only way to access the legal technology was to become Muslim.
Secondly, the Muslim merchants were closely tied together: they met for worship, intermarried, and increasingly belonged to the same Sufi orders. So they naturally tended to do business as a group. If a Malay ruler converted, then he could join this exclusive group (as a I said before, ruler = trader). And when disputes broke out between Malay cities or amongst royal families, the one closest to the Muslim multinational business group had a big advantage. It was a similar situation to the 20th century '
banana republics', where American fruit companies had the power to choose the rulers, without American colonization or invasions.
Thus, Islamisation of far east had very little in common with christianisation of northern Europe which was largely result of political concerns of pagan rulers against ever growing christianity and military campaigns of christian rulers upon pagans. I'm not saying rulers converting to Islam had no effect on the spread of Islam in the region.Yet, the efforts of local rulers to spread Islam is not the same case as that in the colonization and asimiliation of western powers. That's what makes this mechanic exclusive to muslims in the game.
I may have been unhelpful in introducing an example from medieval Christian Europe into this conversation, as I guess that it may not be something you have studied much. I don't think you could describe that process of Christianization as colonization. I think Danish, English, Swedish, etc. people would be very surprised to hear they had been colonized from Rome and assimilated many centuries after the end of the western Roman Empire! They were not colonized, but converted, and just as in southeast Asia, the conversion of rulers was a deliberate missionary strategy.
But as I said, I think the new game mechanism is a good one for this topic.
If you allow me to give recommendation for the subject, I suggest that you do some academic reading starting with Dr. Hee Soo Lee's books about the spread of Islam in the far east. Regards...
As far as I can find, Dr Lee's books have not been translated into English. They have been written in Korean and (translated into???) Turkish. I found only one article in English, published in Turkey, about Islam in northeast Asia (China and Korea). This was very helpful in drawing my attention to an aspect I had not considered before, so thank you for the recommendation. He shows that the first Chinese converts to Islam were Han women who married Arab merchants. Again, we should not imagine young women falling in love with handsome heroes. I'm sure there were many handsome Muslim merchants

, but these were power couples: Han families exchanging their daughters for better access to powerful Arab men. This happened in southeast Asia too and apparently one scholar (Harrison) has argued that intermarriage was the main way Islam spread.
I think it is more likely that a few key marriages were very important in persuading some of the rulers to convert; certainly the Sultans of Malacca used princesses to persuade other Malay rulers to convert. Again, this closely parallels northern Europe: Augustine of Canterbury's mission was only possible because the King of Kent had married a Christian princess from Francia, and later Kentish Christian kings often married their daughters to pagan kings in return for the right to send missionaries. In fact, a young scholar (Wain) has just written a thesis arguing the first conversion of a Sultan of Malacca happened when Zheng He gave him a Chinese Muslim wife!

This is revolutionary if it's true, but his article was published in a fake journal, so it seems other scholars aren't convinced!
Your comments have really given me an interesting afternoon learning more about this subject, so thank you. Maybe I can return your kindness by sharing some articles that I found helpful:
- Syed Farid Alatas (2007) Notes on various theories regarding the Islamization of the Malay archipelago, The Muslim World, 75:3-4
- Ahmad Fauzi Abdul Hamid (2002) The impact of Sufism on Muslims in pre-colonial Malaysia: An overview of interpretations, Islamic Studies 41:3 [this is not Oxford's Journal of Islamic Studies, it's from Islamabad, but as a non-expert I thought it was a good essay]
- A.H.Hill (1963) The coming of Islam to North Sumatra, Journal of Southeast Asian History, 4:1
- Anthony H. Johns (1993) Islamization in Southeast Asia : Reflections and reconsiderations with special reference to the role of Sufism, Southeast Asian Studies 31:1
- G.H. Marrison (1957) History of Islam in Malaya, The Muslim World, 47:4
- Alexander Wain (2012) Chinese Muslims and the conversion of Melaka to Islam, IPEDR 51 [this is not a proper peer-reviewed journal]
I'm not an expert, so there are probably better ones.