I still think the only way this would work (aside from having the hot tub in the green house, would be to capture lost heat. Now my hot tub is very well insulated, especialy above the tub. My hot tub is a self contained tub, the heater is contained in the tub enclosure. But I think this method would work even better with an inground hot tub. Idealy, if the hot tub is not installed yet, you could build an inground hot tub (the heater is seperate with an inground hot tub). Install the just the heater inside the greenhouse. Otherwise, the place I have found the most Waste heat with my Tub, is above the heater. So hputting some sort of heat exchanger above the heater to capture the heat lost from the heater would work very well.

Good luck Drake. There is no inground custom bathtub outa concrete industry, manual or design tome. Just get in there and build what you think best.

Honestly I would call a local pool builder. You are basically wanting a indoor spa. 12 on 12 #3 rebar, with 4 bars at the top and a little thicker 12", and 6 to 8" of concrete/shotcrete in the walls. You can insulate under it, but remember that is a lot of weight, and insulation could crush over time causing it to move. Not really necessary. Running heat strips in the pour sounds like a reasonable idea. Unless water table is high or something don't see sealing exterior. Seal interior well and probably tile it, just like you would do any wet location. Again, call a PB, they could hook you up.

This long and narrow bathroom reminds me of the one I grew up with in Brooklyn. It had the same problems you are facing. I highly doubt there is a radiator in this bathroom. The OP can comment if it exists or not. The large diameter steam pipe in the corner is a typical set up for bathrooms in old buildings. There is probably one thermostat controlling the heat for the entire building. The apartment above does not get to set its own temperature. How warm you apartment is in the winter is determined by what floor you live on. I agree if this is the only bathroom then it should to have a tub. I am not sure if re-configuring the tub is going to lower the resale value on a $1M+ coop in NYC. Putting up the wall between the tub and the sink makes the shower more functional. But it will make the bathroom look smaller and block some of the light from the window. I still think if you are going to move the tub the something like this one at Home Depot could work. It is 6 inches shorter than a normal tub. You will need 54 inches from stud to stud which may be possible once the plaster and lathe are removed from the walls. You could install the tub 8-10 inches away from the window wall. A shelf could be built between the tub and the wall and covered with tile. That becomes a place to hold your shampoo bottles and soap dish. Most of the steam pipe would still be exposed and will keep the bathroom warm even with the shower curtain closed. The shower head and controls stay on the same wall. This will open the space to put in a 36 - 48 in vanity with a granite counter top and a wider medicine cabinets and better lighting. That will give you ample storage space. Something that was not an issue when this bathroom was laid out 100 years ago. Have you asked any of your neighbors if they have remodeled their bathrooms? It would be helpful to get ideas and see how they dealt with these challenges.