Norman,
We just finished with a project similar to yours. Sorry to give you bad news, but the only way we found to get a really nice finish was to totally strip off the old varnish, re-sand the doors and then apply stain and varnish again. You can use most any of the strippers available, but we really like the brand “Bix”. What a lot of people don’t know, is that once you apply the stripper, let it work and then scrap off the varnish, you need to wipe the remaining varnish off with lacquer thinner. CAUTION, the stripper and lacquer thinner are very flammable.
Hope this helps,
TA