I would try using a pair of channel locks,if not able to move then grind flush, and drill with titanium bit inward to recess into the block/stucco. Seal it off and refinish,(if they can rust) they will not without oxygen.
these tapcons are more trouble than there worth,it sounds like but the time you are done beating the remains of the tapcon,chipping in a little ,cracking off the rest and mortaring the hole don't sound too bad,sounds like you've spent too much time on it already.
You can get a Lennox Arbor 5L which is basically an open end gadget with a set screw. But the soft metal of a Tapcon would likely yield before extracting. Grind off the head, jerk the piece out and break off, or grind, the old anchor back to the substrate.
I have no use for Tapcon anchors. I can achieve equal fastening with a quarter inch sds bit in a rotary hammer, driving any combination of 16d and 8d nails, depending on the thickness of the wood.
To me, Tapcons are as useless as powder actuated nail guns. Too complicated and expensive. Too much trouble.
Eh....say Teetor...has my talk got any of those old Tapcons out yet? Hate it for ya.
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