Tires are always a tradeoff, we want it all but that seldom happens. The supper stick summer only tires that are barely more than longer lasting race tires these days give up rain and cold weather grip but do grab pretty well for straight line use and superb cornering.
As mentioned a tire a bit taller than stock will help in autocross due to not having to shift to 3rd gear except on some fast courses and some still might not need it, far better to give up a little lower end and not have to shift as often.
Also a taller tire will have more contact patch than a smaller diameter tire so it helps offset any reduced tread width, not completely but it helps, it is why many race cars run tall tires.
Since autocross and track events as well as fun mountain driving focus more on cornering than off the line grip I would fit the widest properly supported tire you can fit on the widest wheels you can find.
Also keeping the weight down will help a huge amount on all aspects of performance.
The RE-11 is the better tire for the rain for sure but gives up quite a bit of grip when it gets very warm so not a great track tire. From what I recall reading as I was intently looking at all these tires last spring was the Rival seemed the way to go but I would look into this more as you may want the best overall grip but still good in the wet or at least safely drivable.
Take a look at the Rival specs, it is wider than probably any other tire size per size, a 215 is probably as wide as some 225's, a 225 as wide as a 235, etc...... I believe the 215 was 2lbs lighter than the 225 as well, 8 lbs is a bunch of weight where located.
Find a wheel as wide and fairly close to factory offset but compensate for the added rim width, I run 15x9 +35mm and they stick out a bit but rolled fenders and 225 race tires tuck them back in though I had to change the rear camber to make them fit back there.
A tire like the 215 Rival which is taller than stock, wider than other 215decent weight, on a 17x8 an offset of 40-42mm would probably be a good fitment but a bit more looking into it would be the way to go, the 225 would not have as much support and might not even clear in the rear and adds that extra weight as well as even taller and might be to tall for your gearing needs forcing to shift to 1st gear which is not fun for autocross. I have ran events in many states, many types of cars, getting one single setup to do all you wish is sometimes a serious effort but the closer it is the better.
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I love your area, I was there for the World's Fair and originally from WA state, I have shipped a few hundred packages to Blaine and another town in the area for pickup from CA as well. You are from a great place, a very progressive city in an incredibly beautiful area with great weather.