Pick up a copy of Precision Shooting and write to Bill Calfee via the editor. Bill has built quite a number of the top prize winning .22 bench guns, and likes the Lilja barrels. He could probably recommend a chamber for you based on your action with that barrel. I know he likes to burnish his chambers after cutting, with a special tool. It is also worth going back over past issues of PS to learn how he slugs the .22 blanks to figure out which end will be the muzzle and which the chamber, and also how much to cut off the blank at each end? Besides, his folksy writing style makes for an extremely entertaining read.
Regarding the tight barrel, a lot of cast bullet shooters find they need the hard cast bullets about 0.002" to 0.003" over groove diameter for best rifle accuracy, rather than the traditional 0.001" over. It's a statistical observation, not a theoretical notion, and nobody knows why that should be true, just that it can be measured to be so. With the softer swaged lead in the RF it makes sense that number could be bigger. Certainly the soft lead squeezes into the barrel pretty easily, and I expect Dan Lilja has come up with his groove diameter just as empirically as the cast bullet guys came up with their bullet oversizing number. That's good. It means it works based on test experience rather than theory, also.
If you don't want to wait for Calfee's response, ask Lilja. He probably knows what Calfee is using.