Lightmapping + dynamic shadows?

I'm trying to set up a scene where the environments, lights, etc. are static, but my character is dynamic. I've set up each light to have Mixed baked mode. I bake the lightmap, and the static shadows are all there, but:

1. the Mixed lights don't appear as strong on my character as they do without lightmapping
2. there are no shadows coming from Mixed lights

I've tried every possible combination of every possible setting - static and non-static lights, different lightmap modes, different lightmap setups, baked and realtime GI, everything. Nothing works.

Anyone got any ideas? I'm on the newest version of 5.1.