I don't have a clearance spec for you - might want to call CS. On my SM066, the burner is about 1/4 inch below the bottom of the wood box. My wood has never caught fire. I think you can just slightly bend the burner down (carefully) if you need to.
I can't advise on adding wood after the smoker is up to temp. It seems that would delay the smoke, maybe not start it at all.
If you have too much smoke on your product, I would not necessarily blame the smoker heat-up time which should not be over 20 minutes or so. The smoke plume should then settle down to a thin plume, that may come and go as the smoker cycles on and off. I haven't encountered too much smoke unless I use too much wood to start.
Again, don't soak the wood, and use chunks, not sawdust or chips.