One question in between: What exactly does "logic level MOSFET" mean?
The ones I have here have a typical threshold voltage UGS of 2..4 V DC and work fine with an opamp at ~8V DC power.
What would logic level be?
Logic Level as oppose to 'standard' MOSFETs is a poorly defined term. About 20 years ago most MOSFETs required more than 5V Vgs to get reasonable drain current. In those days 'logic' meant 5V so a class of MOSFETs evolved that were marketed as 'logic level' MOSFETs.
The advantage was that you drive these using a 5V supply.
Now it simple means the parts have a low gate threshold voltage. You really need to look at the transfer curves.
Here is a standard MOSFET, the IRF540:
And here is the Logic Level version, IRL540:
Most of the time the lower gate threshold is better, but not always.
I hope that this helps.
Jay_Diddy_B