" Arriving at the boat following a week of shorepower, both banks read 12.8 with no load. Application of 7 amps, (reefer/lights) and the system voltage drops to anywhere from 11.5 to 12.2. Remove this load and system voltage increases back to original value.
Is this normal? "
For a dead battery bank, it is perfectly normal.
The float charge on good batteries should read about 13.6 when you get to the boat and drop to 12.6-12.7 when you knock down the float charge.
The fact that one of yours drops down to 12.2 means that bank is only holding a 60% charge, while the bank showing 11.5 volts is quite dead.
Doesn't matter what you can shake out of it--that bank is dead for any real load use. If you are charing both banks at the same time with the same controller, the dead bank might be the drain that is preventing the other bank from getting more than a 60% charge. GET RID OF IT.