There are plenty of ways to skin this with what you have listed.
Rotary converters spring to mind, basically a DC motor coupled to a DC generator (Which is just another DC motor), WW2 technology, lots of the old aircraft radios used these.
You could also use a motor with a set of cams operating switches to build a flying cap doubler, or even do this with a relay wired as an astable (This will be kind of hard on the relay contacts).
The vibrator was a special case of an astable relay actually designed for this use case, with carefully chosen inductors you got zero current switching and surprisingly good contact life. They were popular as a source of HT for valve based car radios in the 50's.
Am I allowed to take some of the copper wire and oxidise it to get copper oxide? If so I can make a copper oxide rectifier which opens up some possibilities.
Find yourself an OLD book on electrical machines, ideally dating from about 1930, there will be examples of all kinds of cool semi mechanical ways to do the stuff we do with a few chips these days.