Gary,
I too have been looking at the Hawkeye, today actually. I found a .204 in one and it's a really pretty little rifle, walnet and beautiful stock. I have been searching the Internet this evening, trying to find reviews on the Hawkeye as to general accuracy and trigger pull. Then I found your post. I wish more people would respond that know about this rifle.
Years ago I purchased a model 77 in 257 Roberts. Nothing I did could make that rifle shoot well. I tried everything, from various bullets (brands and weight), powder and primers, to free-floating the barrel, changed stock to a composite, glass bedded the action and even glass bedded the entire barrel later. I even sent it back to Ruger and they recrowned it. I really liked the mauser-type action and so wanted that gun to shoot, but it would not. It was a pethetic case, so it found a new home.
I've been Ruger shy ever since.
But, today I found the Hawkeye in .204. It's rather heavy, which I like for my intended purpose - groundhogs from a bench. And, as usual, I like the action and looks of it, but that Ruger shyness remains. If I thought it would be a winner, I would get it. I'm also wondering about the trigger and what might be done to improve it, if anything, or if there are good after-market triggers available. Right now I'm thinking and searching for more facts and data.
Hopefully someone else with some experience with the Hawkeye will chime in.