I agree with most of the posters here. The Ithaca 37 is one of the great classics and I'd definitely keep it. Unmatched in it's handling qualities for a pump gun, IMO. I don't profess to be the end-all expert on the 37, but here's how I see your gun: My resources show yours to be manufactured in 1980...so it will have a trigger disconnect...i.e., no 'slam fire' capability. It also was made after the time when Ithaca specifically fitted individual barrels to individual guns during 37 production. Which means you can find other Ithaca 37 barrels that will work without hand fitting.
At a place like this one:
(And again, if anyone has better information than the above, don't be shy. I think
what I have is correct, but I can't swear to it).
Personally, I would not "Tac out" a classic like the 37. #1) there are not a lot of accessories for them. #2) It just won't 'look right', IMO. I might
get a 2nd barrel from someplace like the barrel exchange, cut it to 18 1/2", replace the bead and consider it "tac'ed". But this is all JMO.
BTW, I have 1920xx, manufactured in 1948. It is a wonderful old shotgun.