Sorry, I should have read your whole post before giving you all of the advice below, which apparently you won't need. Okay, Once you have the neck and dowel re glued, you actually do have some adjustment. The dowel stick is held in place with screws that go through the rim of the reso well and with two pieces of dowel each with a corresponding "doughnut" of plywood that go from the underside of the dowel, to the back, and also through the end by means of the tailpiece screw. Now, say you've set your neck angle too shallow you can actually plane a little off the surface of the dowel stick where it hits the reso well, so when it's screwed in place again you will have more back set in the neck. Of course that means you also have to replace the dowels on the back side with pieces longer by the same amount that you took off the top side of the dowel. That said, essentially you want to set your neck in relation to the elevation of the biscuit bridge that sits on top of the resonator cone. And you also have to take into account how much clearance you have between the bridge/saddle and the reso cover. The best way to set the neck angle is to do it with the reso cover removed, so it doesn't get in the way of your straight edge. And essentially when you set the action for whatever you want (be it for regular finger style or a little higher for slide) you just have to make certain that you have enough clearance between the strings and the cover plate--that would mean your "saddle height should be between 3/8"-1/2" high. Now, I'm going on memory here. Haven't done a single cone for about 25 years. More into tricones now, but the dimensions should still be close to the same. But, as I said, yes, you do have some adjustment, it's just a bit of a pain to do so.
've done three neck resets on vintage Nationals that I owned over the years, a 1933 Duolian, a '36 style O (which I converted from a squareneck to a roundneck, and a 1930 roundneck tricone. Of course, the "dowel stick" was securely attached to the neck in all three cases. In that yours isn't, presents a little more of a challenge.
FROM HERE ON DOWN WAS WHAT I WROTE BEFORE I READ THAT YOU ONLY NEEDED NECK ANGLE ADVICE. Although you don't need the following, I just didn't have the heart to delete it.
First, regarding one problem that you apparently have, too much relief in the fretboard. Several people I know like to plane the relief out of the board and refret. If you're more concerned with the instrument's long term playability than keeping it completely vintage, you might consider what I did. I removed the fretboard, pulled out the reinforcement tube, routed a clean channel in the neck, filled it in with new wood, then installed an adjustable rod with the adjustment nut hidden in the heel. From what I see in your series of photos, your fingerboard is bound (is it a Triolian or a Style O?). Removing the board might mean you have to replace the binding, but like I said, if you value playability over remaining truly vintage, that would be no problem.
As far as reattaching the neck to the dowel, I imagine you've already got an idea for that. If not, I would clean off the old adhesive(s) from both the male and female mating surfaces, and if necessary use a shim to fill any gap that may develop through the cleaning up process, then use your glue of choice to re join them. One way to guarantee a good alignment would be to create a jig that would hold the neck in place on the guitar--at the correct angle--with the the dowel stick in place inside the guitar, held in place with the tailpiece screw and the two small dowel & "doughnut" pads that span the gap between the dowel and the guitar back (I hope this is somewhat clear). Then once you have it all line up dry, pull the neck off, apply the glue, then slide it back in place using the jig to keep it aligned.
I've recently built a pair of wooden-bodied tricones and circumnavigated the dowel problem by simply making them with bolt-on necks. Of course that doesn't help you.
I'm assuming that you're okay with figuring out the neck set angle, relative to the resonator/biscuit saddle. If not, shoot me a PM and we can discuss that.
Good luck. I looks like both a frustrating and rewarding project.