A 19" seat is HUMONGOUS. I had an older, German made Stubben with that seat size, and it was obviously custom made for a very large man.
I'd think an 18" would fit you just fine OP, and I really don't think your Western saddle is a 20". Probably more along the lines of a 16", as Corporal stated.
Most adults ride English saddles that have seat sizes anywhere from 17" to 18". As I stated, a 19" seat is huge and I don't think I've ever seen a 20" English saddle unless it had a 2.5" cutback, which made the seat size 17.5"