Its a bit difficult to understand your scope plots- I can't tell the magnitude of these spikes, it looks like there on a math channel thats reading out in webers? I think the problem is that at these very slow rise times, you're getting through conduction. The driver has dead time insertion between hiside and lowside but it kind of breaks down at these very low speeds. Do you really need to operate at these levels? Another possibility is running out of dynamic range in the current measuring- isn't there a low side current sense below the fets? (CSNA etc.). These can also be tough measurement but if your high speed stuff works ok, you probably have a decent test setup.
I have a question for you. I just bought a Siglent scope (SDS120x HD), what are you using for a current probe?. I have one for my old Tek buts it only for that scope with the smart interface stuff. I haven't bought an I probe in a while, they've gotten really pricey.