Sword curvature is more of an indicator of the period it was made than the smith who made it; kind of like clothes are.....how they are used and fashion to some degree. Sometimes swords have what seems to be a LOT of curvature, then we try to figure out why. The swords don't always tell us though. Google wanted to tell me all about Tommie, though...... I am hopeful that someone will have an oshigata and/or photographs of an authenticated Tomoie, but there seems to have been several different signatures and from neighboring fiefs as well. Anything is a start, but there are few guarantees even if the sword came with a paper.
(Many hours of study later) difficult to find definitive information on the specific mei fragment, although the Fujiwara Takada school was doing great things down in Kyushu. Saw some VERY impressive swords from the Koto time frame. I have not found any references for a smith named Tomoie beyond the Hawley TOM 458 who signed in the specified format, but am not limiting my search to him/them; I am looking for any smith/school who used the format. No bingo yet, just Bungo (a little provincial humor )