The SXP has a back-bored barrel which usually patterns best w/ a more open choke when shooting TSS. I'm shooting a TSS reload of straight 9's/ 8's over 9 1/2's/ and 9's over 9 1/2's, all of which produce great patterns which I've evaluated at ranges from 10 to 55 yards. I prefer a 10" core of 300+ w/ an even 20" w/ no voids. I evaluated the factory choke, a Jeb's .655 and .665, Primos .570, and Carlson's and Trulock .580.
The factory choke patterned well w/ factory Winchester Longbeards, but was inconsistent w/ TSS. Both Jeb's chokes produced blown patterns w/ fliers. The Primos had a nice pattern w/ a tight 10", but was too tight IMO for a good hunting pattern. Both of the .580 chokes delivered great hunting patterns, 300 + in the 10" and an even 20" w/ no voids. I kept the Carlson's and sold the Trulock to a friend who has an SXP and have hunted w/ it now for 2 years. I raised the comb on my SXP and installed a Vortex Venom on a Sumtoy base. I've worked extensively on the trigger and have lightened it considerably, eliminated the creep, but there is no elimination of the "take-up" much like that found on most AR's. I've shot my SXP a lot and the "take-up" on the trigger required before you are set for a normal trigger pressure release and firing is no longer a problem, but I would advise becoming very familiar w/ the trigger set-up on the SXP before hunting w/ it.
