I've spent some time on creating Mughalistan with Hyderabad with vanilla Revolutions. That was normal-normal. And yes, prestige is the biggest problem.
First of all it's quite easy to get rid of your satellite status. Just make your subjects to revolt. Change the ruling party manually a few times and stay with liberals in power. Your conservative population will not like it and will revolt sooner or later. Let them. Let them take your capital and most of the provinces. Save your troops ! Voila, your government changed and you are no longer a satellite. Try to stay a monarchy (watch your reforms). Start that in 1836.
Set your sliders - education 100%, military 100% (you need that prestige). And hope for some nice event. I lucked out - got "unexpected invention" with 8 RP in early 1840's. I think I got steam engine (don't remember) and traded for freedom of trade (which gives you higher income). BTW some German minors are good trading partners, at least for a while. Then you do nothing till the Crimean War starts in 1854. Well, you might try to trade with China and Japan for their claims in Ryukyu and Sachalin (and claim colonies) but you just don't have enough diplo points to get the relations up. Oh, and get raw materials and expand your army. You will need at least 9 additional divisions, preferably more. I go for half cavalry half infantry. If the maintenance costs are too high send them as expeditionary corps to Nagpur.
So, it is 1854 and you watch the British departing for Russia. Wait some time (might be as long as a year). Save your game and when they left for good declare war on Nagpur. Recall your troops earlier of course. Hopefully they went bankrupt maintaining your expeditionary forces. If not, well, that happens, there goes your prestige. The Brits will declare on you, but they are preoccupied with The Bear. If they come back (happened to me once) reload and wait a bit longer with your declaration of war. Now, you can easily annex Nagpur. Or you can just humiliate them to declare again in 5 years (to get some prestige). Of course that will work only if the Crimean War is still fought in 5 years, otherwise UK will finish you. So if you don't want to take that risk annex them. Occupy as many British provinces as you can. In a year or so the Brits will start to offer peace deals. Get the provinces giving you access to the rest of the Indian minors. UK should agree for a deal equal to your warscore (provinces worth 20% for 20% warscore). Get your troops back to your territory. Declare on another minor. Hopefully a bankrupt one. If there isn't any, just take one that is convenient geographically, i.e. will get you access to another minor. Beroda is a candidate, so is Jodphur and Bhopal. UK will declare on you again in defence of their satellite. Declare on other minors as needed to get required provinces. Again occupy as many provinces as you can and get a good peace deal. It might be better not to annex a minor if you don't need their provinces and their capital gives you bonus warscore = better peace deal.
Note that every declaration of war will cost you prestige as the minors are weaker than you. I tried to get all my declarations of war before I made peace deals to lose as small amount of prestige as possible. Still after I got the required provinces and signed final peace with UK I had only about 40 of prestige. Luckily there were some minors around (2 or 3 - Nepal, Bhutan, Kutch) which were not satellites of UK and already went bankrupt. So I attacked them, got a peace deal for 5 points each, attacked them again in 5 years and so on. Finally I scraped together 100 points and WHAM I'm Mughalistan with the most of India and 3 national cultures. I was also a satellite of Germany. And hopelessly behind in technology. And hated by everyone (badboy of 60 or so). In short life was interesting
Now if you don't mind lots of reloads you can achieve this in late 1860's. But I was saving every 7 days during that 10 years long Crimean War in that game. I was avoiding revolts and prolonging the war by reloading if there was a revolt in occupied province or a sudden outbreak of peace. If you do mind reloading it will take a lot longer (1890's) and you will need more troops. And the revolts during wars will drive you nuts
P.S. My 100th post
