Great info posted, listen to it, follow it, will help a great deal and you are far better working on your driving instead of modding the car for now, glad you understand that
There may be a valuable trade off going with either tire. Taller sidewalls can flex more but the 1/2' narrower section width may make up for that. Heavy wheels slowing you down already, 8 less lbs of rotational un sprung weight is a lot more than many comprehend the value of. But, the wider tread width may still be faster though it could be harder to drive at the limit which is what autocross is all about.
If you go to the right forum you can see what experts on the tires have to say, those of use with a lot of experience can help a great deal but if we have not ran a stock class car, ever, with the current tires available on various rim widths like me out of many cars I have setup and ran, our advice simply cannot be the best.
I believe you will learn more and likely be faster sooner with the easiest to drive tires so you can focus on technique which is hugely important in autocross, let a really great FWD or most any really fast driver give you a ride in your car and it will really open up your eyes.
Unless it is really hot out or you are over driving, have two drivers, etc...you might not need to spray your tires.
Best way to take temps for autocross is at the outer edge, middle, inner edge, right after the run, even temps is best, a bit warmer on the inside is usually better than the outside using an infrared meter as the heat is not as deep in the tires like on a road race session. I have done this so much I just use my palm most of the time, faster and it is pretty calibrated after all these years
Another thing that helps, dial in all the negative camber you legally can.
A slight bit of toe out usually helps turn in as well but not so fun on the street as the car might wander and be prone to follow grooves in the road.