Some matters to think about. A "sunk" tabernacle has a lot going for it, I believe - and the aft-facing opening, as you have drawn, is a practical way to orientate it.

The straight trunk, as opposed to the curved trunk you have drawn, will work slightly differently and I am not sure which will suit you best. However, in either case, if the tabernacle is to be 3' deep and the the top of the tabernacle is close to the deck, then when lowering the mast it will have to be lifted up before it can start falling back over the sloped (or curved) trunk. It is not geometrically possible to be otherwise, unless you have an excessively large trunk and a very large slot in the cabin top. If you make a scale drawing of the mast in its starting position, with the heel engaged in the tabernacle, supported by some kind of gallows at the stern, and ready to be lifted, you will find that the angle is somewhere around 20 degrees. This (and the length of the slot) limits the depth of the heel of the mast at the start of your lowering process.

Raising the mast up to a standing position and having it drop down into position will be straightforward (if you have enough power), but to lower the mast it will first have to be lifted until it is high enough to start falling backwards.

The higher you can place the top of your tabernacle above the deck, the less you will have to lift the mast to lower it. If you could make the tabernacle 2' or more above deck and 1' or less below deck, then you will have 3' of bury - and you will have a configuration which might be practical for raising and lowering without having to lift the mast vertically. But you say "The tabernacle can't be too much higher than the deck" so the arrangement is going to include that complication of having to lift the mast partly in and out of the tabernacle. (And also if this means the boom is going to be close to the deck, then it is going to conflict with the SJR if you plan on having the spanned running parrel-downhauls which are usual for this rig. See below.)

So I think that what you plan is do-able, but maybe not quite as simple as "Insert the mast as in image three and push upright and lock as in image four".

I have a 17' boat and a mast which is in a sunk tabernacle. (Mine requires no trunk, as the entire cabin top is open.) I can manage to raise and lower the mast on my own and with no mechanical assistance - ("insert mast, push upright and lock in place") but it is near the limit of my strength to do this. The first part of the lift is not too difficult, standing back near the stern.  But once the mast is at head height - not much higher than the gallows - then things get difficult. If you lift higher you are quickly wobbling at arms length - as you walk forward (careful where you put your feet) the lift gets heavier because you are getting closer to the fulcrum and it gets a bit scary as you get closer to the fulcrum and past the point of no return - until you start approaching vertical and then it quickly becomes easy again.

Your boat is 26' so it seems to me most likely you will need some sort of mechanical assistance to raise and lower your mast. And as pointed out already, you may also need to devise some way of lifting it vertically before commencing to lower it. There are ways of arranging these things.

* Another possibility might be to have the opening in the tabernacle facing forward and having the mast rotate backwards over the rear of the tabernacle, using a hinge or lashing at that point. Then your trunk will be forward of the tabernacle instead of aft, and the geometry is slightly different. A simple scale drawing as above will tell you if there is any advantage. A lot depends on how you plan to raise and lower the mast.

* Have you made your mast yet? If not, and if you are going to have to lift the mast vertically anyway, then I suggest making the tabernacle the full 6' down to the keel, and make your mast about 1'6" longer than your plan requires. Put a loose plug (1'6") into the bottom of the tabernacle, for the heel to rest on. Your mast head will then be at the planned height - but you have 1'6" of "wriggle room" up or down if you find later you need more mast height, or if you decide you need to reduce mast height.

* Do you plan to have spanned parrel-downhauls (recommended for SJR)? In that case the boom must be a minimum of half a panel width above deck plus an allowance for turning blocks plus some allowance for the spans to twist as the boom rotates 90 degrees in either direction. That being the case, the sunk tabernacle could be a couple of feet above deck?

Good luck with your proposed SJR and by all means continue the conversation.