Well, here are two maps of soil temperature regime and soil order. I am by no means an expert on medieval plowing technology, nor of global soil types, but Bulgaria seems to have soil more characteristic of eastern and central Europe than of the Mediterranean. At least from my uninformed perspective, this could indicate that the heavy plow could see some use there, in a territory just outside what would have been the Byzantine capital.
I do not claim to be a real expert either, but I am familiar with Lynn White's theory regarding soil types, the development of the heavy plough, and the way the relation between these two led to particularly noticably increase in effective land use in specific regions. If we take a good map of European soil types, I can illustrate how - and where! - the effect described by White is relevant. The maps you provide are both very general, being of the whole world. Please allow me to post a more detailed map of European soil types:
White's ideas was specifically about clay soil. That's luvisol, marked with orange and the number fourteen. Later studies have backed up his theory, which basically holds that clay soil is very fertile, but also very hard to plough. You need that heavy plough, but once you get it... spectacular production! A more recent sudy into White's theory - which confirms his findings - can be found
here. Another soil for which White's theory would be very valid and relevant is the dark soil found north of the Black Sea, chernozem, marked in brown and with the number six. Chernozem also makes for heavy, but extremely fertile soil. So if White is generally correct, his theory also applies here.
Something to keep in mind: other factors than soil type are relevant. Again, I am no expert, but I recall reading about White's work and it was pointed out that soil in Spain and Greece, though being rich in clay in some reasons, suffered from other factors - such as insufficient hydration - that would make it unsuitable for the intensive agriculture which is, of course, the exact advantage provided by the heavy plough. So we should not get too excited when looking at this map, with its vast stretches of orange and brown.
I don't know much about Bulgaria, but I know it's considerably more hydrated than Greece and Spain. So there is potential there, namely that coastal area west of the Black Sea marked in brown. That's a soil type that would need a heavy plough to be used effectively, and is sufficiently hydrated to be very fertile when that heavy plough is applied there. But it's not very big. And that's, as far as I can tell, the
only area owned by the ERE that could really do with a heavy plough. The primary area in Europe that can really benefit from the heavy plough is that vast orange and brown plain, stretching from eastern Germany, north of the Black Sea, and all the way on to the Urals. But that's all outside the ERE.