To your last question, can offer 10/22 barrels in any format you can dream up. I have been developing specs for my LR PRS 10/22s and they have done very well for me. I have just started looking into 'speed' shooting ... ie rimfire steel challenge and CRPS version... more for something to do in the winter vs serious competition.
When chatting with those who are doing this game, their distances are very short.. inside 50yds so they typically run factory barrels. The size of targets are also very generous. If you are looking at smaller targets at longer distances and accuracy that your factory barrel can't deliver, then I have match barrel options what will shoot very accurately further out
If you have a specific game/course of fire, first I would look at the accuracy requirements vs function/reliability. Some accuracy specs can make things more sensitive to type of ammo used and function.
Then overall weight and balance. I would not see a really heavy rifle as being advantageous.
Can offer you a different 'tactical' contour which is heavier then a sporter but way less then the typical HB. I developed this when the 'AR' looking 10/22s were really popular. Similar contour to an M4 for diameter. Balanced very nicely and was lively in hand.
Not sure if I would bother with muzzle threads as a brake doesn't do much with a rimfire... but you can use it as a front weight to help balance the nose.
I would start by shooting the factory rifle and adding weight to the front of the barrel and see if it feels better or worst. That will tell you how to create a replacement barrel.
PM or email... happy to discuss.
Jerry