As an alternative you could purchase a home repair jack--they're a dime a dozen on Ebay.
Bick4 is not the ticket---there are emollients and oils in Bick4 that would destroy the type of bond (friction) you're trying to create between the leather and the peg.
Few waists don't have hollows underneath the outsole.
No. When the leather is moist all the way through it swells up and the fibers are pushed apart. As it dries the moisture migrates out of the leather leaving those spaces between the fibers. When the leather is in just the right state*, you can firmly hammer the leather, shaping and compressing those fibers down around the peg. You can compress the fibers into a smaller and denser mat than it was when it came from the tannery (usually...depends on how many times and how firmly it was rolled).
If the leather is too dry, hammering the will not compress the leather much if at all.
edited for punctuation and clarity
My conjecture is/was the soles weren't properly finished with enough wax coating burnished...