I wasn't under the impression that either affected conversion rate? Probably the biggest difference is that unless someone already has a viable attempt that I don't know about, some of the exploits are likely to be patched before a Jihad run happens. There is small consolation that Najd might get a unique national idea.
As far as conversion goes: you start with 1 missionary, you can get another from Religious Ideas, and a third from DotF. Taking Jerusalem and Rome will give another two for a total of five.
On the positive missionary strength side, you start with 2%, Religious Ideas gives 3%, as Muslim you can go full Piety (likely to happen in such a run) for another 3%, so that's 8% to start. Then you have a couple decisions: Licensing of the Press Act gives 1% and Unify Islam (DLC) gives 2%. On the more temporary side you have Inquitistor advisor and +3 stability for give 3.5%. So you have 11% to 14.5% per month to work with, not counting buildings, positive random events, and ruler-lifetime decisions.
On the negative side, each base tax is -0.5%---Ile De France will be tough to crack with its -7.5% for example. Shiites and Shintos give -2%. Might be some nasty events, too, but I'll not look them all up now.
Supposing an average conversion rate of 5%, at this rate you would be looking at 600 conversions in 200 years. Considering that a fair portion of the provinces are in the Americas or Sunni already, this doesn't seem too bad. Probably the greatest threat is some high base tax provinces getting a string of events.