Wow guys, thanks for the responses so far.
On the basis of the advice from everybody, maybe the first thing to do is to get a compression test. There's a garage at the end of my street I can probably take it to for that. That'll tell me whether or not the Weber conversion is even an option.
If the compression's okay, I guess that opens up the option of doing the Weber swap. The list for fixing the EA-81 would be along the lines of:
1) Head gaskets to cure the coolant leak?
2) Rear main seal, and possibly the front too.
3) Valve cover gaskets
4) Oil pan gasket
5) Carb itself (requires some manifold mods, it looks like? I haven't read all of the threads yet)
6) Clutch while I'm in there (goes hand in hand with the rear main seal)
7) Adjust the lifters
8) New water pump
9) Ignition issue (it seems to be missing from time to time)
10) New muffler
Now if I get a lower mileage engine from a yard, that takes a couple things off of the list, notably the gaskets, the ignition issue, the water pump, the front main seal, and possibly the lifters (haven't checked a manual/the forum for an EJ-22 to see if they're hydraulic or solid). The muffler and clutch are a given either way.
If the Weber's an option, I guess the question boils down to what's the value of putting time and money in an engine with at least 150000 miles (the odo is stopped there, and I don't know what year it stopped...), versus biting the bullet and getting a whole newer engine.
In dollars, the answer seems to break along these lines:
(Engine + accessories + adaptor + Y pipe mods at a muffler shop) vs (carb + misc gaskets and seals + water pump + any ignition components I'd need)
I know somebody whose dad owns a junkyard (automotive salvage place/whatever), so I'm pretty confident I can at least work it out so I get a running EJ-22 to start the project with, complete with water pump, alternator, etc. There's a clutch shop that re-faced the clutch for the TR-6 when I did that near my office, and I'm sure they can handle changing the holes for the EJ-22.
I suppose absent a compression test this is all idle speculation though. I'll see what the garage can do for that Thursday. I'm sure they're going to love doing the cylinders on the driver's side of the engine. I've changed the plugs, and they're a royal pita to get to with the A/C compressor and alternator in the way.
On the subject of the ECU, the Y-pipe does have an O2 sensor on it, and the carb is festooned with an array of gee-gaws and doo-dads with wires coming out of them. There is, however no ECU attached to the (roughly) Y-shaped piece of metal welded to the bottom of the steering column. There don't appear to be any cut wires, or enough loose plugs to connect to one either (I count about 30 connections in the diagram in the Haynes). Hence the confusion. I'll snap some pictures when I have daylight if you want to see.
On the subject of parts for an EA-81 or EA-82 to do an SPFI conversion (nice guide, GD), I would put my money squarely on being SOL. In Cleveland, salt is the name of the game all winter, and most of the older Subarus around here have long ago rusted into the ground. Mine came from Florida, so it's pretty clean (minus some spots in the bed and a couple places where the undercoating is starting to crack in the seams underneath).
Incidentally, I can solder and read a basic wiring diagram. So can Ross (the willing accomplice), so it's mostly a question of getting the time and tools to do job. Notably, getting the engine in and out of the car. If we can do that, I'm fairly confident we can make it all work.
I'll let you all know how it comes out!