That's an interesting design, I am not really sure why you would be seeing those spikes like that, as it only occurs when switching to the negative half cycle pulling current, the schematic shows that the H bridge stuff looks pretty symmetrical.
Also, it appears that the high-side differential amplifier (high side current sense amp) is redundant, as you could just use the effective 500 ohm resistor between the ground and the emitter of T600 (and also, transformers are normally labeled with 'T', while transistors are labeled with 'Q'. I'd call it Q100 or something.).
My guess as to the problem is software. It appears you are using a microcontroller for the switching of the 4 H bridge devices, and it may be a software issue causing shoot through when switching, say, A and C on, but leaving the load temporarily disconnected from the current source when switching to say, B and D.