You may have to resort to some thin CA to get that sheeting started.

Just hold it in the correct place along the leading edge, and glue it to the leading edge with thin CA from a dropper. Once that edge is stuck down, you can use wood glue along the ribs & spar and then tape, clamp, or whatever method of holding you're using.
As far as the burnt edges of the laser cut parts go, the only place you'll have to worry about it is edges that covering will be stuck to, especially if you're using lighter colored or transparent covering.
One modification I would strongly recommend is the turtledeck. Either replace the balsa stringers with hardwood, such as spruce, or sheet it. 1/64 or 1/32 ply works great for that. Also, depending on how you plan to fly the plane, you might want to enlarge the control surfaces. With some slight enlargements, the SE can be turned into a 3d beast.
And I know you've got an engine in mind, but fwiw, I did discover a couple weeks ago with my friend's SE ARF, that an 1100mAh NiCd pack placed just in front of the 2nd to last former in the tail will perfectly balance out a 70 Surpass on the nose.

:bananahea