My question is - do I need to replace the old battery that is not able
to stay above 12.20 or will this combination work? Also, is there
anything that I can do to "pump up" the old battery.

The plates on the old battery you have left look to be in poor condition,
sulphated. Once the lead is turned into crystalline lead sulphate, there
isn't much you can do to recover the ACID that got used up in the process.

It's best to replace them both at the same time so both series batteries
have the same capacity and will run down together. Try not to run them
dead! That's what tears them up, way too early. If you're setup has a
voltmeter, you can watch the voltage and guess pretty close when it's time
to stop and recharge to prevent them from going too far into discharge.
You'll notice the voltmeter stays above 12V at moderate load for a long
time, then starts to trail off every time the motor load comes on them.
This bend in the voltage-time curve is pretty close to the proper point to
stop discharging them....and recharge.

A 330AH "deep cycle" battery only has about 150 AH of useful power before
you SHOULD recharge it. Running them dead, even the fancy shmanzy AGMs is
suicide!

Larry