225s are super narrow so what you might be gaining in compound and price point you will be losing in section width and contact patch.
Have you considered running drag radials on all four corners? Something like this may serve you better on an 8 or 9 inch wide rim: https://www.tirerack.com/tires/tires.jsp?tireMake=Toyo&tireModel=Proxes+TQ&partnum=55R6PXTQ
This is a lengthy one but I know you can hang.
There are a number of angles I'm looking at with this prospective buy.
First off, unfortunately, I can't use drag radials for the SCCA class I'm in because of the 200 treadwear limit. Otherwise I'd keep the current tires on my 16x8 rims which are 255/50/R16 Hankook C51s.
Secondly, the tires I decided on last night (but haven't yet bought and won't for a while) actually do come in 255&245/50/R16, but what I'm wanting to do is try to keep the section width basically the same as my wheel width. From what I've been reading, 225 & *235 (*which doesn't have a good selection at all) are the sweet spot for an 8 inch rim. Supposedly when your setup is pretty much "square" the tire won't be able to lean as much. I didn't notice that much with my Hankooks, maybe because as a race tire they have a way stiffer sidewall, maybe because my lower driving skill level didn't even think to look for it or know how yet. (Aside from extreme cases when I took too much air pressure out.) But I've definitely noticed this effect with my 235&255/60/R15 Cooper Cobras on my 15x7 T-type wheels. Other than just being able to make the car wobble with a firm push, you can actually feel the rims "traveling within the tire" during quick transitions. Lots of sidewall flex. Granted it is an All-Season.
Thirdly, the first step (looking at 225/55s) will be to get a tire that performs noticeably better than my Cooper Cobras, but still something that I can commute on for long distances and in the rain. No swapping wheels at events would be another bonus. The tire I'm looking at for this is a mid-tier tire around 300 treadwear. I was looking at either Yokohama S.Drive or BFG Sport Comp-2 (the latter of which available in 245&255). They're rated at 300 and 340 respectively. The Cooper Cobras are 440 with an All-Season tread pattern, for comparison. Supposedly the BFGs are better than the Yokohamas in the wet and have a better turn-in, and are evenly matched in the dry. Additionally, I do intend for the car to still be able to get a little loose on me because I've been learning an awful lot with each unintentional slide and push. I just intend to have tires that make it happen only slightly less often than my Cobras. In other words, still be able to get decent practice with slipping but not have it as a constant burden.
The second step (looking at 225/50s) would be to step up to a "max performance" summer tire (SCCA CAM-T legal maximum treadwear (Bridgestone RE-71 etc.)) once I'm finally comfortable with my skill level. How I take step 2 depends on how step 1 turns out. If it goes well and I can stand to lose just a touch more wheel height, I'll consider getting my first serious set of tires in 225/50/R16. If step 1 is lack-luster and I can't stand having my exhaust even one more inch closer to the ground, then I'll save up for a set of 17s which can accommodate more "normal" sizes in that same "max performance" category. I'd still like to end up with ~26 inch overall wheel height in the more distant future, so either way we look at it I'm going to get 17s one day. But I'd like them to be forged aluminum in just the right dimensions, and I still don't know what that's gonna be yet. So having to buy stop-gap cast aluminum wheels would be a minor setback to that goal.
Short Version:
I hear that "square" wheel & tire combos have excellent responsiveness and I wanna try it. I'm not too worried about finishing 1st yet, but I am worried about my severe lack of budget for this season and there's no way my Cobras are gonna make it through another summer. Now's the time to transition.