bigmax - try the TX .224's on paper. You may need to run them .030" or so off the lands. I started with .040" and found under 3/4" accuracy at .030" using the Blue coated ones as well as plain vanila X's. Closer might raise pressure unduly. The TX is supposed to allow closer seating, but even int he 7mm Mauser, .050" off the lands gave sub MOA acuracy. The big cased .22s can pump up pressure pretty quickly as I found with the .22 Swift IMP.
I'd go for the 53gr. bullet (or whatever the TS is) and work on a descent load. It will work if you do.