What factors played the biggest role in the shift of royal power from the Germanic warlords of the early Middle Ages to the powerful monarchs of early modern Europe?
Germanic warlords is perhaps not the correct term to describe those who held political and military power during the early European middle ages. Most held property in fief from a higher lord or even a monarch, and were obligated to fight for that lord or monarch. They often held titles such as Duke, Count, or even Earl. At the time, monarchs relied on these lesser nobles to furnish him with troops in the event of war, and also to fight for him themselves.
The most important factor in the movement to centralized monarchy was the ability of counts, lords, etc. to extend the areas under their influence by means of attacking territories held by others; or held by nomadic peoples such as the Magyars or Lombards. A prime example of this is Otto of Saxony, who defeated the Magyars at the Battle of Lechfeld, and was crowned Holy Roman Emperor by Pope John XII. It should also be pointed out that the support of the church was important. Although many Kings and Emperors were excommunicated for disagreements with the Church, most managed to maintain good relationships with the Popes, and used this factor to extend their own influence.
In England and France the change in relationship between Lords and Retainers allowed monarchs to increase the power under their control. If a nobleman died childless, the monarch claimed the late lord's property for his own. This was particularly true of the Capetian kings of France who over three hundred years absorbed a great deal of power and with that power assumed the right to administer justice throughout their realm.
In addition, rather than demand service and rents in kind from retainers, kings began taxing them. With taxes paid in cash, kings were able to establish standing armies which allowed them to increase their power. With standing armies, they were no longer dependent upon retainers to fight for them or furnish troops; and were therefore able to impose their authority over these same former retainers.
I know you are a history teacher but I believe some of your information is a little off. Otto was the first ruler of the Ottonian Empire (named after him) and the Ottonian empire was a time where Germanic yes Warlords were in charge. I have an Essay for a college paper where this is the prompt, so if the proffesor who has a doctorate in the subject calls them Warlords I think it is infact the correct term.
To answer the question I think that one of the major factors was the Commercial Revolution. The commercial revolution ended up giving the church more power and it created a new class which wanted to be free from the government and have rule over themselves. So the church had more power and the people wanted different rule. I am still working on exactly when the change to monarchs actually happened. I cant find an exact switch in the book I am using (The Making of the West chapter 9). It sort of sounds like it happened around the fisrt crusade (page 328 if you have the book). In my notes I have that after William of Normandy all of the rulers were from France or England. I hope this helps a little sorry if it does not.