You landed what we called back in the day a SMOKE POLE. Personally I didnot like them and most I have seen were really not trap barrels although most would argue with you they were.
From what I remember the majority were stamped duck & goose to help you reach out and touch waterfowl with 2 3/4" shells. There was also one in field grade marked Full and then there was the true trap barrel which was rem part number 6340 stamped TRAP or later on some had TARGET. True trap barrels were also stepped rib if I recall correctly. I don't believe remington ever offered them on a factory supplied gun but they could be had for about 100 bucks as an accessory. I am going to say we bought one in the early 70's or so and probally have not used it since.
Hastings also made one for the 870 and 1100 in 34".
One thing was for sure all of them were very very tight choked much tighter than a standard remington full choked trap barrel thus when you were on the target it was a ink spot hence the name smoke pole.
As far as value depends what you have hastings or true remington, field, duck & goose or trap. I have seen true trap sell for 400 and others for 150 all about who may be looking for one at the time. take care