I wouldn't say that Islam accelerated science, rather it promoted and passed it on. Just as the great Greek Philosophers were saved only because theit documents were written down by Muslims, for all the Greek stuff was destroyed.
I don't know if I agree with the connection between evangelicalism and scientific publicizing. I'm sure that I can't offer a true opinion, lacking too much critical information of the times and people. Its certainly an interesting idea and concept, that would probably require a historian and scientific biographer who focuses on those times to figure it out. I'd need to learn about the motives of Gallileo, Corpornicus (i can't spell that ever), and others that went well away from doctrine taught to science experienced.
"Christianity more or less encouraged philosophy because it was seen as many as way to evangelize the Gospel to the unconverted."
I think nothing encourages philosophy more than the concept of life and death. Greeks didn't need Christianity to form their ideals. Nor did Lao Tzu, Confuscious, or any other Asian Philosopher. "Why are we here?" is all that is needed to encourage philosophy. While Christianity does not act as a hinderance to philosophy, certainly conservative christians as well as conservatives of other faiths act as a hinderance to philosophy, or the exploration of the ideals. You take Lutherans, they made great "philosophers" of the Old Testament, from Wellhausen (he's german, so I'm assuming he's a Lutheran) to von Rad. But this is swept away from radicals that won't open the Old Testament and scrutinize it for what its worth.
My point is, you'll find this openness, and closedness as well, in Judaism, if not more so. Rabbi's are renowned for their study of the Tanakh. It is this openness for philosophy and truth that allows such an attitude. Therefore, I think it isn't as much that Christianity encouraged it, rather it was the spirit in which a faith is taken in, encourages or prohibits the expansion of philosophy.
"Also, the development of Protestantism encouraged the laymen to become involved in doctrines, which might explain why universities became larger and encouraging average citizens to become educated."
Absolutely! Once Luther opened the door to the bible so human beings could read it, not just the monsters of the Catholic Church, the spread of information zoomed up. But the question remains, was it Christianity that caused this, or rather the spirit of Luther?
"It is difficult to agree what role these attributes of Christianity played in the development of science, but in my mind these attributes were absolutely necessary. Again, I don't think it is a coincidence that science developed in Christian Europe."
While science did develop well in Europe, I think it would be a mistake to discredit such efforts in Asia, because I think this young discussion has not yet spoken of the accomplishments of the West v the accomplishments of the East and commented on why certain developments didn't occur where or why it took longer for one development here than there, etc...
Such as discussion would certainly be interesting.