So i would look at this way --- in William of Rubruck's book he references running across Nicean ambassadors in his travel. So lets look at it this way :
By 1200 ad there are many examples of gunpowder being used all over China in offensive and defensive operations. So looking at it you could create a TL like :
1. Nicean monks and ambassadors are sent east (think Justinian and the monks smuggling back the silk worms), in 1225
2. They smuggle back the formula for gun powder (written first in 1030), with powder sample, one hand gun, one bomb.
3. They arrives back in 1245. The eastern part of the empire has few enemies except for weak Turkish tribes, after the Mongols destroy the Seljuk in 1245.
4. Michael VIII begins reconquest and has built a force with grenades, bombs, ships with gun powder weapons fired from Ballista and catapult.
5 Constantinople conquered like in real world. The field forces armed with Grenades, powder arrows, hand cannon, and ballista and catapult bombs defeat Bulgarian, Serbian, and Sicilian forces. City walls and forts are overcome by bomb fire.
6. IN 1263 the invasion of Greece succeeded (in real time his army of 15,000 was surprised by the Latins and fled - here he wins with a unit of hand cannons which destroy the Latin cav)
7. Michael's fleet with the advantage of gun powder defeat all before it and gain control of the Greek islands and the trade with the black sea and Egypt brings in much needed capital. With a strong fleet in the Adriatic sea they are able to keep any westerners from invading.
8. With peace in the west and the Balkans, Michael is able to focus on the next 15 years in systematic conquest in the East. As the Mongols retreat he picks off each sultanate one by one. The use of roaming cav, and gun powder fire power against Turkish towns shows that the Turks have no safe hiding place.
9. In 1281 the Sicilian vespers neuters his main western enemy.
10. Not having to campaign in 1282 in Albania while sick he stays in Constantinople and lives for another 5 years (age 66)
11. By 1295 Anatolia is recaptured completely, the population is increasing, trade is flourishing, gun powder weapons are becoming better to fight cav in the East as well as the hand cannon are becoming larger to better break castles. Above all the fleet is large and accommodates fire power.
Below evolution : 1200 -- 1200 -- 1400s -- 1450's
https://en.wikipedia.org/wiki/History_of_gunpowder