I had the same problem with my 74 Huffy Easy Going cruiser. 13/16 was too small and 7/8 was too big. I tried the 13/16 - 7/8 shim and( while it did fit well ), the steel 13/ 16 post bent the first time out.
So... I purchased a 7/8" 6061 aluminum solid rod. Took a sharp rat tail file to the OD, and slowly filed it to fit. I kept rolling the rod in my hand to try to keep it roundish. After fitting, I used Scott Brite on the whole rod to give it an even finish. Can't tell where I filed it, now. I did not file the whole length of the rod, only the section that had to go into the seat tube. Worked good, took about 20 min. My seat post extends about 12" out of the seat tube, and is 6" into the seat tube. I am 6' 3" 210 lbs., and it has not bent in over a year of frequent riding.
Go with the aluminum rod. It is really an easy fix. BTW... the 18"x 7/8 brand new 6061 rod was only about $13 at my local metal recycle yard.
When you install it, be sure to grease the seat tube and aluminum rod well. Aluminum and steel do not play nice. That rod will freeze in place over time without grease. With grease, it will be fine...no worries.