Trap guns go through thousands of rounds each year, few guns stand up to that sort of use. Some of the Higgins guns were made by High Standard, who made fine target pistols and lousy shotguns. Had one,briefly.
I've seen few, if any, Higgins or Stevens shotgun on a trap line, tho I've seen some in the hunting field that their owners loved.
The Ithaca is a fine upland gun, but a trifle light for trap. The Model 12 is rapidly assuming collector status. Reasonable entry level guns for 16 yard trap would include Remington 870s and their various newer semis, the Beretta gas guns from the 303 on up, and very used SBTs from Browning and Beretta, tho they're pricey.
Or, use the shotgun you have, have fun and accept the fact that it's not perfect for the job...