The 22" max length is not followed much, but check with your local match director(s). However, I would expect a match with 22" max would include the choke. Where did you see that rule? Also the old rule about the mag tube not extending more than an inch past the muzzle is rarely used, so whatever mag tube you want would be ok. Some matches would require you to plug it to 8 rounds, depends, so, again, ask the match director.
The Remington 1100 TAC 4
barrel (22") would be good, but they may not sell that one separately. Be sure to get a smooth bore, not rifled, with the deer barrels.