Hard to tell from the end view what we are actually looking at. You describe this "U" channel and trim piece as one piece. This can't work as both the chrome trim
and serve as and underlay to protect the upholstery from the metal edge of the seat pan. You can't have a solid piece on
both the outside
and the inside. I would speculate that the "U" shaped portion of this piece is merely a means to
attach the chrome trim over top of the upholstery after it wraps around the edge of the seat pan. Now, granted, this will provide
some protection where the upholstery wraps around the edge of the seat pan, so you have several choices:
>Recover the seat and reapply the original trim to the outside. What bike are we talking about? 350? 450? 500? 550? 650? 750? Other?
or...
>Install a protective material around the edge of the seat pan, then install the seat cover. This protective material can be just about anything, either a "U" shaped piece like what was used under the original covering (at least on the later model 750's), or you could take the old seat cover, cut it into 1/2" or so wide strips, and wrap this over the raw edge of the seat pan, gluing it in place. The only problem with this is it may make the edge of the pan to thick to allow the original trim to fit over this thickened edge.
or...
>Install protective material around the edge of the seat pan, then install the seat cover. Then either forego the trim or find a different trim piece. The trim I am familiar with uses holes though the edge of the seat pan with push on clips on the backside to hold it in place.
What about the seat trim in oldhatt's post?
http://www.hvccycle.com/seats.html Is this similar to what you have?