Two things to an EJ upgrade that are the bonus: 1) there's more of them easily available for the conversion or for spare parts! 2) anything is going to be a power up grade over a tired worn out EA82... and 3) it's a power upgrade either way! (Yeah I know I said two, but really it's three)
EJ conversion and "not much work" don't really go in the same sentence - depending on how mechanically experienced you are with all aspects of a vehicle, including the wiring.
With my conversion I took my time to carefully collect parts, do my research then about 18 months (no rush at the time) to get the wiring right. The wiring is the bit to get right, stuff it up and you're in a whole world of hurt. To make sure my wiring was right I floor tested the engine and the wiring loom:
https://www.youtube.com/watch?v=CUjKbPrZDLM
After this it's merging the EJ loom with the EA loom - not hard to do once you know what needs to be connected in the EJ loom, you just have to find it in the EA loom.
Then the mechanical stuff - three ways to bolt the EJ engine to the gearbox - the most common I would say is to buy/make/steal an adaptor plate with the EA flywheel that's had it's crank bolt holes elongated, then it's EA clutch, some have it beefed up, some don't.
The other way is to take the EJ gearbox and use the front cases to fit the L series gearbox in to. I've done it this way - This is basically the same as using an adaptor plate but you get to keep the EJ factory clutch setup and the gearbox still bolts in as it should.
The last way is to fit the EJ engine with the EJ gearbox. Will need custom gearbox crossmember, gear linkages and most likely tail shaft too.
The engine - it can run with the stock radiator if it's a good one. Don't expect to go offroad with this setup as it won't hold up. There are several options - custom, the BRZ radiator seems to be a new one and a guy on the forum here is using a Saab 900 turbo radiator.
Make sure you fit the engine stay rod, otherwise you'll get all sorts of funny behaviour going on.
The engine mounts can be bolted straight in but they'll sit on an angle, best to put a wedge under them to get them to sit properly. The holes on the engine crossmember also need to be filed outwards towards the wheels.
Really though, just about all the info you'll need to get an idea of what's involved has already been written up in the conversion, mods and performance section of the forum.
If you have any questions from there, drop them in here
Cheers
Bennie