In the stock size there aren't many choices any more. If you want to get an all season tire, the best (and most expensive) choice is the Michelin PilotSport AS4.
https://www.tire-reviews.com/Tire/Michelin/Pilot-Sport-All-Season-4.htm
The General G Max AS 05 is a good street tire.
https://www.tire-reviews.com/Tire/General/G-Max-AS-05.htm
The Hankook Ventus V2 Concept II is a high performance all season with average scores.
https://www.tire-reviews.com/Tire/Hankook/Ventus-V2-Concept.htm
The Vredestein Quatrac Pro is an all season that can even work in snow, and aces wet handling and grip but oddly is poor at aquaplaning.
https://www.tire-reviews.com/Tire/Vredestein/Quatrac-Pro.htm
The Kumho Ecsta PA51 has good grip but poor wet performance and poor comfort ratings.
https://www.tire-reviews.com/Tire/Kumho/Ecsta-PA51.htm
At less than half the price of the Michelin is an OK tire, the Nitto NeoGen.
https://www.tire-reviews.com/Tire/Nitto/NeoGen.htm
Since the original summer only Bridgestone RE050A is no longer available, many chose the Firestone Indy 500s, which do have grip but don't have the sharpness and turn-in of the RE050s. They also are relatively low priced for an UHP summer tire.
https://www.tire-reviews.com/Tire/Firestone/Firehawk-Indy-500.htm
There is the Pirelli P Zero Nero which should have been a good tire, but universally seems to be a disappointment in dry weather handling.
https://www.tire-reviews.com/Tire/Pirelli/PZero-Nero.htm
The Yokohama Advan Fleva V701 is a spirited tire that in Tire Rack's test got the best time on the dry track portion of their testing. It wasn't perfect with only average numbers in Wet track handling and braking, but was rated as OK as a street tire in the wet. I need to get new summer tires this year and this might be my choice.
https://www.tire-reviews.com/Tire/Yokohama/Advan-Fleva-V701.htm
The Kumho Ecsta PS31 is a middling performance tire.
https://www.tire-reviews.com/Tire/Kumho/Ecsta-PS31.htm
If you opt for summer only tires, you should consider getting some 15"x6" wheels and putting 185/60-15 snow tires on them. That's what we do and we probably get less winter than you do in Akron. The lack of grip you are experiencing with the Indy500s is because it's been cool/cold lately. Not quite cold enough to damage them but cold enough that the tread compound has less grip than a hockey puck.
Temperatures even down to freezing don't damage summer only tires; that happens at temperatures a little lower, say 15-25 degrees. But if they get that cold you do have to let them warm up until it's been above 40 for a long time (a day) before you are clear of the risk of cracking from the rubber crystallization. But driving in the temperature range of freezing to 45 degrees or so is risky because of the hardness of the compound at those temperatures and lack of traction.
As evidence that just being in the temperature is OK, look at cars like the Mach 1s I saw at a Ford dealer sitting on the lot this week (or even the FiST back in the day) with summer tires on. They wouldn't do that if sitting there would risk a $2200 set of Sport Cup 2s. But driving on them below 45? No.