Some restorers have described that "dirty stripper" technique here in the past, Norm, but I've never tried it. Adding up bits and pieces from a variety of posts in this thread encapsulates my approach: strip, TSP clean-up, chemical clean/bleach, sand, sealer coat of thinned varnish. Only then do I start replacing old wood (but I may have already removed some bad parts). Applying a sealer coat of varnish gives a good idea of what the wood will ultimately look like under varnish. So using that as a target and testing on scraps or just the ends of my new wood sanded to its final level (220 grit for me), I stain/dye to get the best match possible. Sometimes I'll apply a sealer coat of highly thinned varnish or shellac and then apply stain first if wood is prone to blotching, uneven staining, or highlighted grain that doesn't match the old wood's appearance. Staining new wood before installing prevents stain from darkening or changing the color of the adjacent old wood. That said, sometimes I have no choice but to stain after wood is added; in that case, I use good artist's brushes to stain only the intended wood.
Never having tried the method of stripping after installing new wood, I can't comment on how well it works. Maybe it's great. I just worry that if it doesn't work as hoped, then I may have a lot of very careful staining to do. Plus the stripping sludge might not give the color that I'd like to see on the new wood. Just seems more straightforward to do it before installation when the color can be matched using a wide variety of stain/dye color or color combinations, and so that only the new wood gets stained. Finally, I like to get all the old finish and other junk our of the canoe so that any new wood makes good contact with clean old wood (I'm thinking, for example, about the ridges of varnish, sand and other debris that can be built up on the planking along the edges of old ribs).
Different strokes... just sharing one person's approach and rationale.
Michael