Would appreciate the help of a lighting guru

Might be a simple solution. I don’t know.

I’d like to give my character a torch. So far I’ve got a temporary mesh and pointlight set up.

The problem here is that due to it being simply one pointlight, the torch mesh right below casts an enormous shadow.

(The huge square shadow is from the temporary torch mesh)

I’ve also tried various other locations. Inside the torch mesh will obviously remove the mesh shadow entirely while multiple pointlights evenly distributed around the torch mesh result in similarly ugly shadows.

What would be the best way to tackle this problem?

Disabling shadowcasting on the point light is one way, disabling shadow-casting on the torch is another.

Try to offset light from mesh, and make it animated.

Simple point light gives you constant lightning, but torch fire is more dynamic
It must move, vary its intensity and maybe color.

I think you should try to spawn point lights inside torch fire particle system. This will give you lights moving with particles and controlled color.
Here is documentation Particle Lights | Unreal Engine Documentation

Or use blueprints to move light using interpolation to random location inside some range.
Also try to add light function material to it.

Anyway, first of all find good reference for that.
As for me, here is good one