Thanks for the pictures. Even with them, it's always hard to give remote advice, but let me try.
First, I measured my own mast. I can't currently raise it, or access the mast partners (deck opening), but I can see traces on the mast where it rubbed against them over the decades. For my mast, these traces are at approximately 29" from the bottom. There's about 1" from the backing plate under the deck to the top of the "lip" around the partners. Not sure, which of these corresponds to the rub marks.
Also, my mast sits on a "mast jack", basically a big circular nut on a thread, that is used to raise the mast against the stays to put tension in the rig. That makes my "mast step" taller than yours, by at least one inch. Still there may be a small difference in deck height, but that wouldn't worry me much.
The two tracks that you observe are for the boom and for some spinnaker or whisker pole (if the "track" on the front end of the mast is about 10-20" long).
The DS is used with spinnaker poles mounted to a ring (or two, if you want a choice in positions). Unless you have a spinnaker pole that works with the track on your old mast, I would not bother with reinstalling it and switch to a ring (if you ever want to fly a spinnaker that is, or use a whisker pole).
A whisker pole is used to pole out the jib, a spinnaker pole is used with a spinnaker. Both would be used when sailing downwind. (If you are as new to sailing as you claim, you can safely skip worrying about these details for now and retrofit them during one of the coming winters when you've mastered main and jib and are ready to take on the next challenge).
On your new mast, I see only one block (for the jib) near the spreader location, and I don't see a mast ring. I see some small fittings at half the spreader height on the side of the mast, not sure what those would be. Detail picture?
I take it (hard to see from your pictures) that the sail that you have sets in the same kind of slot that you have in the new mast, with only the gooseneck riding on the track. In that case you should be able to move the track over to your new mast. The widening of the sail slot that you show looks like the mast got bent at one point. Assuming that it was carefully straightened and shows no other sign of stress, I'd expect it to be fine. I don't think you should have any problems raising the sail and I don't think it will "pull out" at that spot (not if the luff is tensioned correctly) so you may find this a cosmetic defect only.
One of the pictures shows o the floor of the boat somethings that looks like a sliding gooseneck. I guess, what we are seeing is one end of the boom. The screw seems to attach to a bit of line intended to go through the tack of the sail? The DS boom has a pin for that purpose.
Since the mast profiles appear to be the same, your tabernacle should work: the oval piece should hold the upper part of the mast in place, and everything is supported by that rather massive plate. Do the slots allow the arrangement to hinge? If not, you may find a hinge more convenient.
Also, there's nothing inherently wrong with using a keel-stepped mast. You've already managed to insert it once. There's a bit of home-made gear I have on mine that makes that process easier. You could retrofit that and never have to cut your mast. (Purists find that keel-stepped masts sail better).
Here are a few pictures:


What you see is a circular base, a gate hinge, a wooden block and a bit of aluminum sheet metal forming a sleeve. You start with the thing folded down, insert the first 6" or so of the mast into the sleeve, hinge it into vertical position and then drop it onto the mast step. Something I can easily do single-handed. You appear to have enough clearance between deck and the lowest cleat to allow for such a contraption.
(You will also note the bent aluminum strip around the front of the disk: it's there to keep the jib sheet out.)
The place where I stashed the full write-up appears to be temporarily or perhaps permanently offline: here's at least the drawing.

- MastRaiserDrwg.jpg (21.93 KiB) Viewed 33879 times
The hinge is the large detail on the right. Also shown is an A-frame that can be used by anyone, no matter how short/tall, to raise a mast. (I built one and then decided to retire it until I'm old enough to need the extra support).
You may have to measure the length required for your stays. That would depend on your spreader widths and there may be the odd inch of difference between the way a mast fits your boat and how it fits a DS. I believe DR marine can make stays to order and they will be able to tell you where and how to measure.
About your sails:
Ratsey & Lapthorn is a British sail making company based in Cowes on the Isle of Wight, England and they had a loft in the United States.The loft was on Schofield Street on City Island, in the Bronx.
That seems to date them a bit, but what matters is not so much the chronological age as past usage. Still, more likely than not, you might be better off with a new set (always assuming that fits your budget). You find suggestions here, or check the list of suppliers for DS sails on the main DSA website "daysailer.org".
I'm sure I forgot something; there's a bit of detail here, but if you are methodical you should be able to figure things out.