Rep Weaver - Adding on more warp?

Howdy folks! Y’all have been so helpful with my other questions I thought I’d bring you a doozy.

I have a set of rep weave rugs I’m working on. I thought I could get three out of the warp, but I’ve got two and can get a bit more, but not a full rug. I’m going to wind 2 yards more of a warp for the third rug. The warp is 8/4 Maurice Brassard cotton.

My question is: do I wind this warp and treat it as a new project? Someone at my guild suggested I tie the new warp ends to the old warp ends and then beam it. I think I can figure out how to do that (it’s hurting my brain a bit as to how I’d keep all the ends organized but I’m sure I can figure it out), but I’m wondering if it would actually work with such a warp faced weave?