I'm a little surprised that varnish remover didn't thoroughly dissolve the
varnish - which leads me to wonder if you are dealing with some kind of
shellac or lacquer rather than actual varnish.  If it is lacquer or shellac,
methanol (methyl alcohol; wood alcohol) will remove it.  However, alcohols
will not dissolve the mixture of gum resins found in varnish.  For that you
would need some kind of hydrocarbon solvent - which is exactly what
commercial varnish remover is.  You could also try mineral spirits, or
almost anything sold as a degreasing agent.  There are also a good number of
pure solvents that will dissolve such materials readily.  Many of them are
too toxic, too flammable, or otherwise too dangerous for me to recommend,
and all of them need to be handled with care - which means good ventilation,
and minimizing skin exposure.  Also, all hydrocarbons are flammable, some
far more than others.  Keep them away from open flames and possible sources
of sparks - like electric light switches and electric motors!  That having
been said, xylene (dimethylbenzene) is one of the RELATIVELY safer solvents
(when used with appropriate precautions) that will dissolve gums readily.
Toluene (methylbenzene) is somewhat more active as a general solvent, but
also somewhat more toxic and flammable than xylene.  These are best used
outdoors if possible, which is also true of any such compounds, including
regular varnish remover.
Paul M.