With direct drive motors, you have to make a pretty big compromise somewhere:
* Two smaller motors (same total power): drastically less torque per wheel
* Two larger motors (>2x total power): somewhat less torque per wheel (still don't have gearing!), cost, weight
If you're adamant on avoiding the solid axle, I think a good-ish solution might be hub motors on all four corners. That way you're far less likely to depend on a single wheel to get you moving.
Or alternatively, a locking diff in the rear (forget about LSDs). They usually provide some gear reduction, so you can skip the chain and drive it directly with the electric motor.
In short, the solid axle is a really good choice that you would be hard pressed to replace, without making a sizeable compromise somewhere.