MOSFET switched H-Bridge ideas required

[devguy]

I have the circuit attached that uses an H-Bridge to drive an emitter coil at 125 kHz. It reversed direction every 1/2 cycle to result in 0 DC average voltage across the emitter.
The P Channel Supplies Power, while the N-Channel switches in the required load (changes current through emitter).
The P Channel on one half the bridge switches on at same time as opposite side of bridge N channels.

The emitter does not provide a DC path so the first problem is that Charge stored in output capacitance of the P channel does not fully discharge until next cycle is part way through (and therefore clashes with same-side N fest switching on, causing excessive heat and loss of power). The 1k discharge caps have been lowered to 330R and this helps but I cannot lower then further or the minimum power setting is too high for my application.

Second issue is the R/C time constant for the N channel fet switching is causing the input to driver IC to be turned into triangle waveform (I can fix this by moving switching to input of driver and let driver directly control the N channels.

So, I am looking for ideas for a typology that implements a full H Bridge to retain the 1/2 cycle change of polarity but also enables the current through the emitter to be adjusted digitally.

Even a programmable current source might work but not sure how best to set that up for bi-directional polarity.

If I use only the totem-pole output (P chan/N Chan like TC4490) and only drive current 1 way, it gets easy but I end up with an average DC across the emitter and loss of power (every second half cycle is 0 volts instead of -11.3V)

Thanks for your ideas.