The bridge produces nearly double the 3.3V. You measured 6Vp-p. Then the current in 20 ohms is 300mA and the current in 23.6 ohms is 254mA.
But your tuned LC circuit does not pass the original squarewave, it passes only the fundamental frequency that has none of the harmonics. I guess each half of the waveform is 0.707 times the 3V peak which is 2.1V. 2.1v/23.6 ohms= 89mA RMS.
Can your AC current meter measure the high frequency accurately?

 

Ok, so since it didn't make any sense to me. I found the spice model of this h-bridge and simulated it. And there should be 6.8Vpp according to the simulation, which I don't get.
I really think there is something strange going on with the coil itself. I will try to use different coils with different caps.

 

The simulation software and Spice model do not know that your Mosfets need a Vgs of 4.5V to 10V to fully turn on.
EDIT: The sim model has "typical" specs. If you buy many of them and they were made on different days then one might have typical or better specs.
If they are all made at the same time then they all might have minimum spec's.
They will all work fine if you feed then a Vgs of 10V.