A topic worth studying
Yes, Byzantium - meaning the Balkans and Turkey - is largely uncharted territory in terms of halakhic literature. And there is surely need for more research on the topic.
But there are a number of reasons why so little has been done. For starters, there is not a very large amount of material. According to a quick search of the IMHM catalogue, most manuscripts in Byzantine script and halakhic content are Karaite. Of the rabbinic manuscripts, most are copies of well-known works from Western Europe.
Next, Byzantine Hebrew is markedly different from the Hebrew used by most medieval rabbis. It is often quite difficult to make it out.
The paleography of Byzantine Hebrew script is still being developed.
Byzantine rabbinic literature did not have much of an afterlife, because the communities were swamped by Spanish refugees in the 15th and 16th centuries. Therefore there were fewer opportunities to copy manuscripts, and many were surely lost.
One other factor to keep in mind is that the geographic boundaries are rarely enforceable, and some Byzantine halakhic discussions have been dealt with under the rubric of Italian halakhah (the study of which is not in such great shape either).