How should I handle old wallpaper over top of lead paint?
Definitely read up on the EPA 'renovation repair and painting' rule.

Option #3, the 1/4" drywall, is likely to produce the best and cleanest results, at the cost of loss of room space and alteration in the look of all your trim.  You'll have to extend all outlets also.  Of course that sounds suspiciously like what happened last time. Eventually your room will be solid wall covering with no center.

Option #4 sounds attractive if that texture on the wallpaper will really hold the joint compound.  I'd run a test with and without the primer/sealer.  Remember worst case here it cracks later and you redo it all with #3.