Right, 1A/ns * 7nH = 7V, so good luck with that.
Such is the problem with leaded parts.
The higher drive voltage of SiC helps reduce the impact of lead inductance.
SMT components perform better (D2PAK has about half the stray inductance of TO-220), but leadless components are required for absolute maximum performance. This is why GaN devices are available almost exclusively in CSP, BGA and DFN packages.
A perspective you should consider: switching impedance. If you're switching 320VDC at 80A peak, that's an impedance of 330/80 = 4 ohms. That's quite low. Most structures (device pins, PCB traces) are in the 50-100 ohms range.
4 ohms at 80ns (one full cycle), is 3.2nF and 50nH. We really only need 1/4 of a cycle, allowing up to 12.8nF and 200nH! So this doesn't sound too terrible, if you can just find devices with Kelvin gate terminals to overcome the source inductance problem. There are some D2PAK, TO-247 and 264 style devices that offer this, and also SOT-227 modules if you don't mind the cost.
Otherwise, consider increasing the inverter impedance by wiring multiple channels in parallel. This raises the switching impedance of a given channel, putting it closer to the characteristic (transmission line) impedance of the connections, minimizing their inductive or capacitive impact. You still want a lower impedance (i.e., less L_s, more C_oss) by some factor, to keep the peak voltage down (I_pk * Zsw = Vpk). So, say, Z_inv ~ 100 ohms and Z_sw ~ 25 ohms.
You can intentionally add capacitors to increase C_oss and decrease Z_sw in that way, but it's probably preferable to trap that energy rather than dissipate it, i.e., use a dV/dt or peak clamp snubber, the energy of which can be recycled immediately (quasi-resonant snubber) or dumped into a common rail and another converter used to put it back into the system (heh, the electronic equivalent of a sewage pump I suppose?).
Also, when you have multiple channels, you can consider driving them independently, yielding perks like phase interleave which reduces input and output ripple current.
Note that a phase-interleave converter (buck/boost/whatever) must have independent current control, otherwise one channel can pull slightly more PWM% (due to timing differences between channels) and blow itself up. Approach it as a series of transconductance amplifiers, outputs wired in parallel. Command their output currents based on a common current setpoint, from a single voltage error amp. This architecture is fully scalable, and gives full voltage and current control, making it particularly suitable for, say, bench supply use.
If you're doing something with a single huge AC output, like an induction heater or RF amplifier, you can't really afford phase interleave, but you should still have 0° power combiners between inverters, to account for slight differences in propagation delay. (Or for the RF case, other angle combiners are reasonable, allowing you to cancel out some distortion; but, this doesn't really mean anything in a class-D context that's already "100%" distortion.)
Tim