The T05 trigger is a nice trigger. No need for a T06.
I had one of Tony's kits in my 52 and it totally transformed it from the lumbering hunk that it was into a rifle that was totally different.

Mine was a .22 ultra carbine too.
With Tony's help it was rebarrelled with a Rapid 7 anschutz .177 barrel. Not an easy job but very doeable.

If you want the best for the 52 contact Tony.