Interesting question to which we do not have a clear answer (making the question all so more interesting!)
I would say that the period to which LI is the most similar is not the renaissance but late antiquity. Let's consider that late antiquity is characterized by:
- the end of classical world empires and the emergence of smaller political entities as the norm (with the notable exception of the Islamic Empire of course)
- the organization of, or emergence of, world religions competing for global supremacy
Add to this real-life late antiquity trends LI's specificities:
- strong resilience of cultures, religions and dynasties throughout centuries
- the importance of the solar theme
Combining these trends, if I were to design a EUIV start scenario, I would basically consolidate the most "promising" political entities giving each of them a stronger "national" territory, with fewer small religions but still some of the really old ones like Luwian represented by one of these more powerful states, with a clearer monotheist trend for all of them. So you should have a strong Arian Carthage; a strong Ballist entity in the levent.
Nothing would prevent the progress of sciences like we experienced during the late medieval / renaissance era, but not presented as a re-discovery of knowledge from the antiquity as was the case IRL. Also nothing would make it a more powerful trend in Western Europe. In fact I would, very personnaly, make the Hellenistic States of Central Asia and the mix Iranian-Greek world, at the connection between China and the western world, the centre of technological progress. The Magellan of this world would depart from the Persian Gulf.