Right... shouldn't be too far fetched then. Might even look at a 20 gauge. With the shells and chokes going these days, lots of people are killing turkeys with 20 gauge out to 60 yards.
Haha semi-auto and "not breaking the bank" hardly go together IMO... I have heard decent things about the Mossberg 935 and have personally shot the Stoeger M3500. How much are you wanting to spend?
Remington 870 is the only way to go in my opinion without breaking the bank. Mine holds a great pattern with a Kicks Gobblin' Thunder .665 choke... shoots very true out to 50+ yds. Which is plenty for me