Geraint,
First of all, thank you very much for your input. It is really appreciated.
You beat me to it, as I was about to add to my original post:
The blade is indeed signed Yamashiro Daijyo Minamoto Kunishige (山城大掾源国重) and as you mentioned, I was also told that the smith's name is Ichizo (市蔵), the younger brother of Otsuki Yogoro Kunishige, the most highly-regarded swordsmith in Mizuta school (Oyogo Kunishige school, lead by Master Otsuki, Bitchu province). I was also told the blade was forged in the early Edo period, around 1645-1648, so everything is indeed pointing to KUN1026 (Hawley).
The thing is I've also found 2 other smiths who signed their work Yamashiro Daijyo Minamoto Kunishige; KUN1037 and KUN1113 (same school, different era). I completely trust the source, but any directions or leads that could help confirm the smith would be appreciated.
Here's one more pictures for your viewing pleasure.