Hey congratulations on driving again!!!
I never use an overcheck. It is even against the rules to have one in the American driving society's rulebook.
The only reason I might consider one is If the horse is an incoragable grass eater. If your mare is not a grass eater, dump it. Hopefully the bridle you bought has a noseband, you need one of those.
As for bits, I most always drive in a snaffle, I have a mullenmouth liverpool bit but hook the reins on the snaffle ring. I have the liverpool part for shows, at home I just have the mullenmouth snaffle, I drive in a fullcheek snaffle, a pelham bit on the snaffle ring., a broken kimberwick, not in any holes ie the snaffle ring. D rings, O rings, Eggbuts. Without the overcheck, most bits are okay.
Get rid of the overcheck, I know you have it loose, so just don't use it. I have a box of overchecks that I have never used.
If you feel you must use the overcheck, just hook it to the driving snaffle, that is the least harsh placement.