I cut out a mock-up of the doublet and got it basted together. Hopefully I'll get a chance to try it out tomorrow. I cut it out of some burgundy cotton that I had lying around (it turned out to have been sewn into a chiton -- no big loss to take it apart). If it fits, it'll make a perfectly serviceable lining. I'll probably line the sleeves with acetate if I still have some around, just to avoid friction when putting the thing on.