Old painting with linseed and stand oil underpainting is starting to drip

Yikes. It definitely sounds like you are using way too much oil.

Stand oil is more concentrated than linseed oil so I’m unclear why you would use that as a base.
This is the opposite of the fat over lean principle where you use a smaller oil to pigment ratio for your first layers.
I would definitely discontinued this practice.

You can try removing the drips with gamsol and then touching it up.

I don’t think varnish is going to help, sorry.