I'm not quite sure I agree with the seige improvements for the Ottomans - ultimately they acquired the monster cannon that took Constantinople because the Byzantines couldn't afford it - meanwhile, the same seige weapons got stuck in the mud on the way to Vienna, resulting in the Ottoman failure to capture the city...
And upgrades to seige (if I'm reading right, correct me if I'm wrong) will eventually lead to the Ottomans having a modern army (or artillery), which they should not have, as they were so corrupt and spread out by the end that they couldn't afford it...
What impresses me about the Ottomans was that they continuously fielded (at least through Suleiman's time) large and well-led armies. The practice of the Devshirmeh (blood tax - the Ottomans required one child from Christian (or other non-Turk) families) created / feuled the Janissaries. They also had an unbelievable string of great sultans...
Would it be possible for any conquered city to provide one (or 2) Janissary(s), thereby creating / expanding the Ottoman military? Call it the Power of Devshirmeh (or some such)...
If that's not possible, perhaps some general / leader power or something - sorry, I'm not really up to speed on Warlords and what it adds...
You could give them cannon, etc. to start, so they have the siege ability, but I don't really see upgrades to seige weapons as the right UP...
Just some thoughts...