I would cut your strips so they are 22" long, then two are basically the equivalent of one regular sized strip (44", minus seam allowances). Plus 7 2.5" strips would be 17.5", so you only have a half inch of waste

I'm still swirling the ideas for a JRR quilt in the back of my mind, and I hate cutting off that 6" or whatever it is in the beginning, because that seems like such a waste. My thought is that I could probably re-attach that 6" at the opposite end, but maybe that's not a good idea for some reason my brain hasn't realized yet.