The two-piece bolt and non-match chamber work against it. The sub-minute 77-22 has not been built, except maybe by accident.
I have a 77/22 made in 1984 IIRC and it has open sights on it. I paid $400.05 for it with all the shipping from Gunbroker. That included a straight tube Bushnell scope that I left on it. I tried a 2x7 but like the old straight tube better.
My favorite target is a sheet of paper that has a bunch of 1" squares on it. Using the cheap federal bulk ammo from WM I shoot 10 shot groups that will stay inside those 1" squares. Time after time until the barrel gets fouled. Brush it out and you are back in business. I haven't tried any other ammo. I never saw the point. So I guess i bought the only accidental 77/22 that Ruger built that will shoot. And its box stock too.
I am sure it was a fluke but a 30 yard 5 shot group I fired had 4 rounds in a very slightly elongated hole with one pulled shot less than a quarter inch out.
Another suggestion would be a Marlin 981T. I have one I paid $173.00 new, including tax for it and its almost as accurate as the 77/22 I have. Plus with the tube mag it will feed shorts, longs and long rifle rounds. The stock is synthetic so you don't have to worry about banging it up hunting with it.