Strange Byzantine (?) Coin

I respectfully disagree: this is an overstrike.

Specifically, this follis, probably of Constans II (SB 1004 or similar; I can't quite read the mintmark), was struck over an earlier coin (probably also a follis, less likely but possibly a 30 nummi, hard to tell), Constantinople mint, probably regnal year 24 (X/X/II/II), in which case almost certainly of Heraclius.

What you read IINO is actually CON II, the mintmark and part of the regnal year of the understrike. XX is also part of the regnal year; as I already mentioned, I can't quite read the true mintmark. The place where ANNO would have been is lost in the details of the understrike.

I have some Arab-Byzantines with a sharp-top M, and if it looked like an Arab-Byzantine I would have said so. It does not. It looks like an overstrike.

EDIT: the obverse legend ends COhST. If this is Tiberius Constantine it should have had a bunch more letters in it; if it's Constans II (or later) it's too late to be Arab-Byzantine.
EDIT 2: some Arab-Byzantine issues put the mint name in this place, but offhand I can't think of any plausible Arab-occupied mint that would match the lettering.

I mean it's not like I have all that much more experience than you do! Even in this area, I suspect. (Maybe if it was something like wire kopeks...)
In this case I basically immediately saw some relevant legend (mintmark and regnal year) turned 90 degrees and realized it had to be an overstrike.

Some further possibly-relevant clarification: it is not in any way uncommon for 7th century Byzantine coins to be overstruck on (slightly) earlier issues. In fact to the best of my knowledge most of them are.
So when you see what looks like a 7th century Byzantine coin but some details seem out of place, there's a good chance they're actually part of the undertype. (Though sometimes they're part of the overtype and the strike was just that weak!)

In my opinion, it's a coin of Constans II (SB1004) struck over an earlier issue, perhaps of Heraclius (SB 810?). Some attribute SB 1004 to Heraclonas. I don't think it's an Arab imitation although imitations of both types are known.