I was going to walk away but I can't help myself here. I'm going to start by saying y'all should watch this video from 1938 (yes 1938)
Now yes it is a solid wing of an airplane and well sails on booms are not solid wings on air planes but well... whatever.
Back to the link I posted earlier, there's a really nice visual in the last picture:
Basically what happens here is as the AoA of the trailing flap increases, the flow starts to bifurcate and whip around the front of the foil. If there was no foil in front, then as it whips around with higher velocity, it would probably separate and you just get a bucket load of drag as the video above shows. But there is a foil in front so the front foil helps to keep the flow attached over the back of the back foil. if that slot wasn't there and it was one continuous foil, then you probably also get separation (i.e turbulence and drag)
That point of bifurcation on each foil is the point of highest pressure on that foil. So by having this series of flaps and slots, you can increase the pressure under the wing, with increased flow attachment on the top, higher AOA, more lift, and less drag.
There is a point where this stops working and that's where you can no longer maintain attached flow across the outside of the wing.
So what about boats?
On a yacht, the jib acts as that leading foil helping to keep the flow attached to the back of the main. As long as you can keep flow attached to the back, you can in theory keep winding that main to windward. In doing so, you move the high pressure point further aft in the sail and further accelerate the flow across the back of the main as flow bifurcates from the front of the main and around the front of the mast.
An interesting experiment would be to put a whole bunch of tell tales around the front of the main and mast about 1/2 m above the boom and see if you can see the contra flow around the front of the mast.
Now as you go towards the hounds, the jib gets progressively smaller relative to the main so the main acts more and more like a cat rigged boat. Cat rigged boats, without a slotted flap on them somewhere, don't like high AoA without a lot of drag, and so without twist, the mid and top of the sail will start to stall.
Overlap vs Non-Overlap
To me, this is no-brainer for boats with non-overlapping jibs in light to moderate airs. As long as you can keep the flow across the back of the main going. Overlapping rigs it should still work I would think but you'd have to get the trim right on both sails, and I think it would look more like this:
Some benefit, but not as much as having the slot there.
Bathtubs vs Rocketships
To me, for any easily driven hull form, old or new, upwind this is a no brainer in light to moderate and flat waters. I think the challenge here will be maintaining flow. You need to maintain flow over both your keel and rig packages. A lightweight boat in sloppy water may struggle. An old long, heavier boat with a big chorded keel may actually fair better. I don't know. Slow fat bathtubs I'm not so sure but should probably still work in flatter water I would think. If the boat pounds to a stop then that's a different story, you need to reattach flow to everything. IMHO that's where the slow bathtubs will suffer
This is not about trading height for speed, it's about milking that extra few % out of your rig package albeit within a very small groove.
You don't get height by simply pointing in that direction, you get height by buying it with flow over your rig and keel (ie. speed). boom to windward helps give you that bit of extra camber out of your rig in the bottom 1/3rd as a whole package giving you more lift with roughly the same drag profile (as long as you keep flow attached). It stops working when either the breeze picks up, you can no longer keep flow attached, or you become overpowered and you need to drop the boom down.
As to lazy helmsmen, well, if the helmsman has to work then you are doing something wrong. Yachts work because a balance of forces. If you are fighting against those forces then you are putting the handbrake on somewhere. Upwind you want to create a neutral to semi positive feel to the helm. Boom angle is one of the tools at your disposal for doing that. Use it or not, I don't care....
If you want to argue I'm wrong, go fire up Java Foil, Sail7 or similar and run some simulations. I guarantee you that's what the big programs have done. Theory is nice and all as well, so back it up with some practical on the water testing. Again guarantee that's what the big programs have done.
Will it work for your boat? I don't know, but I can certainly tell you why it *should* work and where it may not