Cases like that - where there's a dissolve transition in a shot that's otherwise being replaced with a better source - don't come up TOO often. Though some of the Storyteller episodes come to mind. In those cases, the VHS source was restored as much as possible, and the VHS and DVD sources matched as closely as possible, and at some point the VHS source dissolves into the better DVD source. In the case of The Soldier and Death, there was always a major special effects error present in the first shot of the episode anyway, so I reconstructed it with new effects to make that less obvious. [Basically they had tried to extend the shot with a portion of a different take, and the seam is obvious.]
Yes, I can generally make the two sources match. Often they already do match [since NTSC sources tend to stay the same size, most of the Jim Henson Hour episodes are already from many different NTSC tapes playing at the same time]. Other times the better source is from PAL, and takes work in After Effects to match with the NTSC - like in the commercial breaks of Miss Piggy's Hollywood or A Celebration of 30 Years. Actually there's a ton of work I put into these things that most people wouldn't notice. Little Muppet Monsters episode 1 was particularly crazy.
Any work I did on the Muppet material is simplistic compared to the very complex work I did when restoring the film The Thief and the Cobbler, but I have plenty of tricks I can use to make sources match if necessary.