so did you literally just drill & tap out the plugs for the same size of binding screw or did you do it for a mm smaller than the screw?
if you did it for the same size you're not going to have the best grip of the screw to the core even if you managed to tap it perfectly the same as the thread for the previous hole as there will be give in the old glue you've dislodged.
If you did it for a mm smaller you're still going to have the same problem that there will still be old weakly bonded glue holding your screw to the core.
I would have said just to leave the plugs in and re-drill 1cm back from the old mount as either way you did it you're going to likely rip out the bindings eventually.
what was wrong with the old bindings, and how did you manage to macgyver them into being magically fixed?