I know this is an old thread but I have some info that may help other still looking.
I talked to an Ithaca rep the other day looking into finding a shorter replacement barrel for my model 37 with a 28 inch barrel and he told me they do not make a shorter replacement barrel for the 37 featherlight but if you have a 37 made after serial number 855,000 then you will not have to have any fitting done and next year they are going to start making replacement barrels for their model 37 Defense in lengths 18 1/2" and in 20" inch. like he told me if you can wait a bit you will be able to buy a new one because all model 37 barrels interchange after serial number855,000. or you can do what I did and buy a used one and cut it down to the legal length of 18" inches, but like I did not go any lower than 19 inches myself because tape measures "read different" depending on who is holding it! also that is 19 inches from the action not the thread lock in the action like it should be. I like the shorter barrel because it makes it easier to maneuver inside. and I kept the stock barrel for hunting.
new barrels from Ithaca price at 12 gauge M37 field barrel with brass bead sight in 26" and 28" lengths - $224.00 for on with out the vent rib or go on eBay and pick up a used one for less than $100.00. just make shore it is after serial number 855,000.
Here is the link to Ithaca that i Used just follow the link under Resources tab to gun info request, fill out the info and a rep will call you back shortly like with me it was less than a hour and i got a call back.
Hope this helps