How can I boost research?

My Holy Roman Empire spans Western Europe from Iceland all the way to Mali and from Portugal all the way to the Caspian Sea. My dynasty has successfully reclaimed the Kingdom of Jerusalem and held it against invading Sunni hordes while defeating Slavic incursions into Western Poland and subjugating the Norsemen in Scandinavia. Not surprisingly, the greatest threat I face are my own vassals.

Having quickly assimilated many varied cultures into the HRE, I find myself constantly shelling out gold to disgruntled kings and dukes because I can't be Irish/Anglo-Saxon/Germanic/Lombard/Greek/Arabic/African/and so on and the -16 hit combined with a constant -25 for my heir being raised by whomever can do the best (not by culture) makes it difficult to make any progress financially.

The best way to fix this is to raise my Tolerance level in the Cultural Research track. However, even with my capital in Constantinople and 3 cities with maxed out universities, my spymaster grabbing research points in Damascus, and my chaplain hitting the books like crazy, I still only manage a meager 1.25 points per month.

Is there some way to speed things up a bit? It would be a lot easier to take all of Northern Africa and tackle Russia if I don't have to worry about hemorrhaging gold to my vassals.