Get some of those anchors that you beat into the concrete with a
hammer. I don't know what they're called,

Rawl calls them Zamac Nail-Ins. Their holding strength is incredible
when they're used correctly, but the OP says he already has the holes
drilled.

For that, you can go with a lag shield.

but they have a lead body
split in half, and a nail sticking out of the top. You slide it into the
hole and beat the nail down. This spreads the lead body and anchors it
firmly into the concrete.

Like the others though, I see no reason to not trust TapCons or similar
concrete screws.