I'm not familiar with the Lindberg "Sandpiper," but I have the general impression that it's intended to represent something on the order of a War of 1812 privateer rather than a revenue cutter.
The extant information about American sailing revenue cutters is frustratingly scanty. So far as I know, the only actual surviving plans are the ones reproduced in Chapelle's books. It is clear, though, that the Joe Lane was not a member of the Morris class. The Joe Lane (officially Joseph Lane, but everybody seems to have called her "Joe") was a beautiful ship with extraordinarily sharp lines. There's a detailed plan of her in the National Archives; Chapelle published a redrawn version of it in his History of American Sailing Ships. The amount of detail on that plan is quite extraordinary; it shows the paneling of the interior partitions and the locations of the doorknobs on the water closets. What it doesn't show, for some reason, is any hint whatever of the ship's armament. It's generally thought that she was armed with some sort of small swivel gun amidships, but there's no indication of any gunports (which, given the amount of detail on the other parts of the drawings, surely would have been shown if they'd been there). The drawings for the Morris class don't show the guns either, but do make it clear that the ships of that class had shoulder-high bulwarks with gunports cut in them.
We've discussed the old Pyro/Lindberg "Independence War Schooner" in several threads here in the Forum. In its initial form it was based on an old Model Shipways solid-hull wood kit, which MS sold under the name Roger B. Taney. In The History of American Sailing Ships, Chapelle listed the Taney as being a member of the Morris class, and the MS kit was based on Chapelle's drawing. Chapelle later found another drawing in the National Archives with the specific name Roger B. Taney on it. That drawing, which he published in his later book, The History of the American Sailing Navy, shows a vessel that's similar to the "generic" Morris class plans, but differs in several details. The Model Shipways kit originally appeared, I think, between the publication of the two Chapelle books, so it didn't take account of the new drawing - and neither did Pyro when it copied the MS kit in plastic. (The owners of Model Shipways used to refer bitterly to "Pirate Plastics.") So the Lindberg "Independence War Schooner" actually represents - reasonably accurately, if without much detail - some other member of the Morris class. Maybe the Morris herself.
Several model companies have offered the Joe Lane in kit form over the years. She was, in fact, among the tiny "ships in bottles" made by Gowland and Gowland that Revell distributed briefly in the first years of its existence. Bluejacket currently offers a nice plank-on-frame wood kit under the name Jefferson Davis that's obviously based on the Joe Lane plans. I'm not sure whether the Davis and the Lane actually were sisterships; I suspect that may be one of the many tidbits of Revenue Marine history that nobody knows for certain.
Caveat: the best published source on all this stuff is Donald Canney's book on early American revenue cutters, and I don't have a copy of it. Don Canney is a fine scholar, and his work can safely be regarded as being as close to "definitive" as anybody can get at the present time. If anything in his book contradicts what I've said, it's safe to assume that he's right.