Just be aware that if any restricted part like the FP breaks, Ruger will not touch the rifle if it has been rebarreled with a custom barrel and you'll have a very nice looking fence post because they will not sell their restricted parts to anyone.
I know of two people who now have useless Mini's because ruger would not fix them. They went all the way to the CEO and no luck.
If you have your barrel Cryo treated (I recommend 300 Below) and then put a strut on it, it will shoot far more acurate and the stringing issues will be gone. Also have the barrel re crowned and then take really good care of the crown.
If you want a heavier barreled Mini, get one of the new Tacticals.
I've got mine shooting .9", 5 shots at 100 Yds. Your not going to get a lot better from a semi auto ruger, no matter what barrel is on it due to the design of the weapon. It's not a target weapon. A Kel Tec 5.56 folder will shoot consistant 3/4" groups if you want a semi auto that shoots under 1 inch. Really neat weapon also, check it out. It's the jack knife of weapons.
Want to shoot one hole groups, buy a Savage target rifle.
Do not buy the Shilen Bull barrel. They have a lot of problems with them and it will not improve the accuracy, trust me on this one.