Mysterious Byzantine Overstrikings

I recently picked up these two Byzantine Constans II Follis coins. I was able to identify the first coin as a Constantinople mint Constans II Follis SB 1005. The second coin is a Syracuse mint Constans II Follis SB 1109.

The issue is that I cannot figure out what these coins are overstruck on. For each coin I have attached photos of both perspectives of the strike along with my id cards.

For the SB 1005, it almost looks like its overstruck on a cross potent Caliphate AE Fals (look at the reverse for what looks like a cross potent with circle thing at top). But this wouldnt make any sense with the timing.

For the SB 1109, it looks like its overstruck on a facing bust Follis of some sort but its very strange- theres some crisp Greek lettering to the left of what looks like the top of a face on the obverse. The reverse looks overstruck on a large Follis "M".

Any help figuring out these overstrikes would be much appreciated!