What do you get if you substitute capacitors on the output of the gate drivers, rather than the actual FETs?
With caps of similar value to the gate-source capacitance of your FETs, you should be able to see how the drivers respond on their own, with no complications from FET drain (load) coupling.
If the waveforms are still messed up, it's some resonance in your circuit; if not, it's likely an effect caused by the FET drain-source capacitance, which opposes the gate drive as the FET switches fast.