Hello Daox,
Neat to see a mod like this go forward!
For either welding or brazing, you will need to do extensive cleaning of the empty case (pull out bearings, gears, everything) - perhaps a pass through the cleaner that your local aluminum engine/transmission/cylinder head rebuilding shop uses? Hit the surface with an abrasive flap-wheel first to take off the heavy corrosion.
Brazing *may* happen at a low enough temperature to avoid warping the case. Your welding supply shop or local welding house may have the experience to know for sure. If low enough, you can maybe get by with just a good de-greasing spray on the inside/gear/etc. (still need aggressive cleaning on the outside) to get the trans fluid off the spots that will get hot during brazing, so as to avoid a trans fluid fire and/or coking up the gears/bearing/shafts/etc.
Maybe find a nice used housing that's not as surface-corroded as yours? Or at least as a spare?
Another possibility: Use high-temperature-resistant epoxy. No warpage issues and you may be able to get away with just a vigorous surface cleaning and no full dis-assembly of the trans.
Yet another, or an adjunct to the epoxy version: design your second skin to have flanges all the way around. If you can, get those flanges to lay flat on existing through-bolt surfaces of the trans, that nice rib between the trans and the differential, etc. You'll want a vertical rib along the long smooth side of the trans (opposite the diff) to keep that edge from bowing up. Drill and tap the case to allow bolting down your second skin - use the bolts as the primary strength connection, and the epoxy as the bulk fluid pressure seal. Leaks can be patched with a bit of grinding and some more epoxy. If your second skin is stiff enough, you can use a sealant instead of epoxy.
You also have the possibility of using EGR-valve controlled exhaust blowing through your transmission housing second skin envelope rather than using coolant. Much lower pressure! No pre-warm from thermosyphon action block-heater heated engine coolant, but the failure mode is a minor exhaust leak, and you can shut off the EGR valve if it's a problem while you figure it out.
Note: When pressure testing whatever you end up making, do so with a liquid, pressurized using a hydraulic pump or cylinder. The failure mode of a crack or similar is thus a stream of liquid and rapidly dropping pressure. City water pressure is generally about 60PSI, FYI.
*Do not pressurize it with air.* That creates a shrapnel hazard.
Air-over-water is probably safe enough, if you have minimized the air volume, and keep below ~45psi. Basically replicating how cooling systems are pressure-tested. Do the math on pressure vs. surface area to see what you are up against.
Off-topic of sorts, in that they are not your "fluid heated jacket directly bonded to transmission case" idea:
ar5boosted suggests an off-the-shelf transmission cooler heated electrically. If going electric, I'd use a tube/plate cooler with a flat adhesive "oil sump heater" wired in parallel with your block heater, rather than using the 12V electrics. Alternately, put said cooler in a box you can fill with heated engine coolant, or just get a liquid/liquid heat exchanger. Either way, make sure the cooler is mounted between the fill and drain levels of the transmission, or at least below the fill level and add a second drain at the low spot.
Did the CVT version of the Insight have a transmission cooler in the radiator? You could plumb to that and use a lift pump/filter combo, and a spring-loaded check valve inline right where the fluid goes back into the transmission housing to make sure the pump/lines/cooler stay full of fluid and doesn't all drain back into the transmission housing, messily overfilling it. Harder to get this type right, though.
Yet another another possibility: Either tap two more holes in the transmission housing for bulkhead fittings, or use "T" pipe fittings on the existing fill and drain holes, and fish a piece of metal tubing through the transmission housing. You need access to the inside of the transmission housing and will need to remove all of the gears, bearings, etc. to do any of the welding or brazing options, so this isn't really much more involved mechanically. Route the tubing to miss all the gears, etc, and make sure it passes through the main sump area. Run your coolant through this tube. To figure out what fittings to use, check out how the in-radiator transmission coolers are hooked up. IIRC, they thread into the plastic from the outside. Probably a form of compression fitting. Probably want to use stainless steel or aluminum. Copper/brass or galvanized/aluminized steel may also work - see what the in-radiator transmission coolers are made of.
Good luck!