I wouldn't recommended protecting against shoot through by monitoring the current. Shoot through protection should be by designing the gate drive stage so it can't shoot through, no matter what the microcontroller or whatever is upstream tries to do. The resistive sensing may still be useful for short circuit protection if the LEM sensors aren't fast enough in case of a phase-phase short, or in the case that one IGBT has already failed short and you want to avoid a bang.
That resistor should be acceptable. It has more inductance than say an SMT resistor would, but I'm assuming this is a high voltage inverter (hundreds of volts), so L*di/dt voltages won't be as big a problem compared to a low voltage inverter. For an inverter of this size, you will probably have current slew rates on the order of 0.1A/ns, which is 10nH*0.1A/ns = 1V across the inductance of the resistor, so you won't be overvolting the IGBTs due to this. Your current sense circuit must filter these spikes without tripping though.
You definitely will want to connect the gate drive returns directly to the IGBT emitters, not to the node on the capacitor side of the the resistor. Any inductance in the emitter path is very bad for gate drive (L*di/dt voltage during switching cancels out your gate drive! This could form an oscillator in the worst case).