Should be able to find a bigport one - as most of the 4AGE 16v are the big port variant. The small ports were more common on the newer 4AGE, like the ones used in the AE92 Corollas. Smallports actually make good power up to 200HP and better for N/A setups, but beyond that and for boost - better to go to the bigport. But I agree - trying to source this locally, you'll probably find more small port 4AGE heads.
That doesn't mean that the smallport is poor in comparison - just easier to get there with the bigport. Just means more tuning on your part to hit those power levels.
As for eliminating wheel hop or atleast reducing it greatly is part engineering and part art. Biggest issue is limiting the motion of the wheel in relation to the chassis (toe changes) and understanding the dynamic processes that cause the toe to change. Being FWD doesn't help matters either. Springs, struts, sways do nothing to control wheel hop. Torque mount inserts (motor mount inserts), unequal length and/or heavy duty driveshafts, beefy steering knuckles, urethane mounting bushings instead of rubber, rod ends or spherical bearings at key suspension points - can all help in reducing the chance for wheel hop. Tire choice as well - the sticker the tire, the worse wheel hop can be.
As for tire - 205 will go up pretty fast with even half that much power. If you got a drag radial - it might be able to hold up. But you are likely looking at "tubbing" out the front end to get max traction. That will make the car pretty much useless in an autocross event. Another option is to dial back boost at lower RPMs, so that you are not burning up power spinning those wheels. Here FWD helps a little, since more weight is placed on the drive wheels. But weight transfer is not optimal in a FF setup - so it is a give/take sort of thing.
Width can be as wide as you want. Since you have basically a rolling shell, you can stuff a big of a tire as you want. Widebody is the easiest way - tire just sticks out further. If you are looking for a sleeper look, then you'll have to move the suspension points inwards to make more room for a larger tire. That said, there are a couple of 7th gen Corollas running a 225 tire on mildly lowered setup without major clearance issues. If you ran a spacer - like a 10mm one, might be able to stuff in a 235, maybe a 245 tire. Still, a DOT legal drag tire, would offer quite a bit of grip. As long as you don't sidestep the clutch on launching, should be able to put some power down.
AWD is an interesting idea - 100-112HP per tire. Be one hell of a swap - not sure if the investment to make it work will be worthwhile in the end. The weakpoint there will be with the center differential and matching transaxle. The Celica ST165 and ST185 were available with 5-speeds, so you do have standard shift options. Corolla SR5 All-Trac sedan/wagons were also available with a 5-speed.