Accurately amplifying a number of current sense transformers
Am I thinking this through correctly?

And

The SCTs are current output type, producing 50mA on a 100A load. The
maximum burden resistance is 10Ω, thus the voltage signal generated
from the voltage drop over that resistor is ±50mV.

Here are a few points that might influence the choice: -

50 mA through ten ohms produces 500 mV. Hence the gain required is only 4 and the DC offset problem you originally alluded to might not really be a problem.

The TL081 will not be a happy bunny with the inputs at 62.5 mV above the most negative rail - the lowest the input can be from that negative rail and still work is 1.5 volts.

The InAmp circuit will need input bias current bleed resistors to 0 volts/mid-rail for it to work correctly. You have to provide a DC current path for InAmp inputs to work correctly. Given the circuit you show, there is no DC path. It's a rule.


Personally, I'd go for op-amps and a decent and low output impedance mid-rail generator that can be shared amongst all your circuits: -