Hello Thridtuck,
There were at least two Kunitakes from Heianjo. The older Kunitake (mid-1600s) has an excellent reputation, but the signature is different from yours in both style and in how the name was written. The more recent Kunitake (late-1600s) had a completely different signature from yours. I'm fairly certain of take (武), but it could also be nari (成) or tatsu (辰) or even toshi (俊), or some other deceptively similar kanji.
So, it could mean a few things. I'll put them in order of likelihood:
1. I'm misreading the final kanji (the one that has been obscured due to the placement of the peg hole.
2. The sword is a forgery.
3. The Kunitake of your sword is completely unknown, or extremely minor.
There is no mistake in Heianjo-ju (平安城住), So if the sword is no fake, it was made in the Kyoto area, or made by someone who came from the Kyoto area.
As above, I am not certain of the last kanji - but I am certain enough that I can rule out other possibilites. Unfortunately it doesn't help much - I will keep looking. The kuni (国) is so distinctive that it should help identify the smith. I guess there was no paperwork with the sword? And (longshot) you don't know the name of the officer who your great great uncle helped? Possible to get a picture of the tip of the sword?
Don't spend top dollar yet. But also don't muck around with it (don't handle the blade, where moisture from your hands could cause rust). Don't try to scrape off rust spots.