I guess I'm not going to make your choice much easier, but I will tell you my experience.
Like your Integra, my Protege used 195/55R15 tires. Those were my cars summer shoes. When I got the car in 2002, tires in that size, winter or summer, were very hard to find, and the winters available were more than I wanted to spend. The minus-1 option was 185/65R14, which incidentally, the base model Proteges came with. Tire choices in this size was plentiful. So that size ended up being the winter boots for my car.
With the winter tires on, I did not try to push the car to any of its handling limits, but that said, aside from a softer ride, and little less responsiveness on the steering, there wasn't much lost in most driving conditions. There was some very slight squirminess, but only when you started to push the car hard, and not something that I found to be bothersome at all.
Summers in 195/55R15 were the awful Potenza RE92 (V-rated). My winters were Kumho KW-11 in 185/65R14 (T-rated).
Sounds like you would only want to go T-rated as your lowest speed rating. Any less, you'll be unhappy. Probably an H-rated would be a better choice for you. And if you really can't sacrafice much in handling, stay with 195/55R15 (choices are far more today then back then).
Could the Hankook IceBear W300 be your ticket? They are H-rated, and probably available in both the 185/65R14 and 195/55R15 sizes. People who have used them love them. I can't say personally, but in your shoes, I would consider them.