I think you are getting the paint stripped better than it really needs to be. There was just too many coats of the old paint on there to do a good paint job over the top. You just need to get most of it off to be able to paint over it. You will need to provide good ventilation and wear a chemical respirator when sanding the cabinets. It's certainly to have lead in the paint. Lead was once used as a pigment in white paint.
Most of the voids and defects you could fill with a fiberglass filler. Where the casing is suppose to be nailed to the jamb you might take a piece of 2x4 and a heavy hammer and see if you can close the gap. Then it could be caulked.
Where the drawer, I think you could repair that one instead of building a new box. Since the bottom is thick and nailed to the underneath side you could remove it altogether. Then put some blocking around the inside of the box at the bottom and insert a piece of 1/4" plywood. Then because of the overall width of the box is too wide for side mount slides you could put undermount slides. I believe the thickness of the drawer bottom would give you enough clearance and if not it would be pretty close so you might be able to enlarge the opening a little to make it work.
The end of the door where it has wood rotted out I would try to chisel out as much of the rotted wood away as you can and cut a piece of solid wood to glue in there.
Some of the doors no longer fit the openings right. You might cut them where they are aliened with the openings again. The larger gap won't matter as much as being true to the opening.
There are 12 cabinet doors (24 sides) and all but about 6 side sides have been stripped back. All the frames and cases have been stripped. Leaving some of the primer or paint on them is fine as after the scraping and sanding it wont telegraph through a new paint job. The next step is a deeper stripping of the profile details of rails ands stiles, which will just take some patience and is the last stripping operation left. Then some filling and patching; then tuning the refitting. Yeah, I've been using Bondo primarily and a touch of Ready Patch. (Btw, instead of stripping one technique I used a few years ago on some cruddy baseboards in a hallway was to skim coat them with Ready Patch and then sand the Ready Patch flush ... because they are at floor level and seen from 5'-6' away, they look perfect.)
The baseboards are all stripped. The sheet metal sink cabinet has been stripped except for some a few touch up spots ... and it's doors. For the latter I was planning to just grind them off and make two new doors from wood ... however, I think I'm going to revert to my 1st option which was to strip them and try filling/smoothing the dents with Bondo (if that doesn't go well I'll make new ones and get new hinges). It's a good area to practice my nascent body-filling skills and I can screw up without serious consequence. An educational opportunity.
The drawers are shot. I only posted the one pic but they are missing several tails from the dovetails (one joint is missing nearly all
the tails). I've recently got some new soft maple for the drawers and it has been several years since I've cut dovetails or done any quality hand tool work ... so I'm actually looking forward
to that ... it'll be fun
as opposed to the labors of stripping. As mentioned, I've already sourced some extremely nice Blumotion soft-close slides for the two drawers. All of this is a sort of warm-up to get re-familiarized with my machinery and hand tools after a long sabbatical, to tune them up, plus make the acquaintance of some new tools (ex. I recently got a 100 year old Stanley #80 scraper and totally adore it), learn their use, improve my skillset, and set the stage for some furniture design and fabrication.
Uniformity of door-to-frame gaps are a concern, I'll tackle that at there tuning/fitting phase.
I've got exceptional respiration equipment (and have done damage there in the past), including acid gas canisters for the respirator, a supplied air system, plus a serious exhaust fan. This time around I got a correct pair of PVA gloves for dealing with the methylene chloride, instead of pickling & dissolving my hands in the inadequate PVC or rubber gloves.
I also have a seriously outfitted spray setup with top quality guns (but will likely brush on the cabinet finish) except for the metal sink. There's also a dumb waiter and other period details that have been stripped and will be sprayed. It's nice to keep a lot of the kitchen's stuff from the original era, for example I love the look of the cabinet latches (I'll need to source new brass ones) which would be lost with overlay doors.
Overall, it's getting knocked out.
The remaining obstacles are sourcing brass hinges (no luck at all on that and it's seeming hopeless) ... and finding a suitable crown molding.