How do you deal with the baseboard cap sticking out past the casing at the plinth block?

Before you shave anything, dry fit the casing and plinth together and step back. Plinth blocks are supposed to stand proud of the casing a little, that's the whole point of them. If your cap face and plinth face line up flush with each other, and the casing sits back an even amount on both doors, that's actually the traditional look and a lot of old houses have exactly that detail. What catches your eye might just be that you're used to seeing everything flat, not that it's wrong. So check the reveal first. Hold the casing against the plinth, eyeball the shadow line, and make sure it's consistent top to bottom and matches on both sides of the jamb. If it's even, I'd nail it off and move on. The cap running into a plinth that's slightly proud reads as intentional. The version that looks like a mistake is a cap that's proud of the plinth, because then it just looks like sloppy measuring.

If you genuinely hate the proud cap, you've got two fixes. Easiest is to relieve the back of the cap for the last six inches or so where it dies into the plinth. Block plane or even coarse sandpaper wrapped around a scrap, take the thickness down so the face transitions into the casing thickness before it hits the block. Keep the profile intact, just thin out the back. The other option is back-cutting so the profile dies out entirely before the casing, but that's fussy work and honestly harder to make look good than the reveal approach.

On order of operations, install the plinths first, then the casing between them, then run your base and cap into the blocks. Nothing about your profiles is incompatible, you just haven't decided which piece owns the front plane yet. Pick the plinth and cap as the proud layer and I think you'll be happy with it.

I ran into basicly the same thing last year and the detail that ended up mattering was the thickness of the plinth itself, not just the cap. If your plinth is thick enough that its face sits proud of both the casing and the cap, the cap can land on the block slightly recessed and the eye reads it fine, but if the plinth and cap end up within a hair of each other you get that vague lumpy transition that drives you nuts. Also worth checking your drywall out at the jamb, becuase if there's a bit of a crown there the whole assembly can sit forward even when your measurements say it shouldn't.

Following this one because I'm about to do the same thing around my windows, except with an apron under the sill instead of cap molding, and I'm guessing the same proud-vs-flush question is going to bite me there too. One thing I'm wondering about the back-relief idea, since I've never tried it. If you thin out the back of the cap over the last few inches, does the profile end up paper thin at the top edge where it meets the block? Mine has a pretty shallow cove and I worry I'd sand right through the face before it looks like anything. Maybe that's why the back-cut version exists even though it sounds fussy.

On my last house I ran 7/8 plinths against 3/4 casing on purpose, so the block owned the front plane and the cap landed flush with the block face. Where the cap died into the block I scribed a line off the casing face and planed the back of the cap down to it, maybe an inch of relief. Took two minutes a door and the profile still read fine. Since your casing is loose, I'd nail a plinth and cap together at one door first, live with it for a day, then commit to sixty feet.