JanniS, sorry but I don`t completely understand your "test bench".
For example, what is the purpose of the current source ?
Why do you have three inputs ?
At which node is the L-C circuit connected?
Regarding single supply: Are you not aware that in most operations the opamp is used with TWO supply voltages (+-Vsupply) ?
This has the advantage that the input does not need any bias voltages (except a small offset correction in case of missing feedback).
According to your diagram, you operate with one single supply voltage only.
Here are my recommendations:
** Open-loop measurements (normal operation with symmetrical supply voltages):
1.) Inv. input grounded, small dc voltage at the non-inv. input swept over +-5mV (10µV resolution)
2.) Fix the dc voltage at a level which gives approx. zero dc output.
3.) Add an ac source in series to the dc source.
4.) AC analysis gives you gain and phase.
** Alternative (without dc offset correction)
1.) Place a large inductor (100H) between output and the inv. input. Thus, you have full dc feedback (no dc offset problems).
2.) AC analysis with an ac source at the non-inv. input.
3.) For single supply operation of the opamp put the ac source in series to a DC source of 0.5*Vsupply.
Supplement/Correction to point 1.) Place a large capacitor (100F) between inv. input and ground.