Temperature and the availability of oxygen are the keys. Increasing the temperature the shop should speed the curing process, but as Rob indicated, you could have an incompatibility problem with your epoxy. Also, if the epoxy hasn't fully cured (possible in a cool shop), it can inhibit the varnish from curing.

Below are a few additions to Paul's comments:

: Here is why: Varnish is a resin dissolved in a mixture of solvents.

It often includes oils as well.

: Some of the solvents evaporate
: quickly. Other solvents do not evaporate, but they thicken, coagulate or
: polymerize in the presence of oxygen.

That's not exactly correct. The solvents evaporate, which is the initial strong chemical smell when you first apply the varnish. They don't contribute anything to the curing of the varnish, they're just there to make it thin enough to apply easily. The smell is largely gone within the first hour or so after application (though it takes longer for all the solvent to evaporate once the surface skins over), replaced by the lingering scent of oil/resin. The oils and resins combine with oxygen and polymerize, at which point the varnish is cured. This can take, hours, days or even weeks, depending on the environmental conditions, the formulation of the varnish and the thickness of the application. Warm temps and thin coats accelerate the curing process.

: The second and subsequent coats will dry much faster. The underlying layer of
: hardened varnish will soften due to the action of the solvents in the next
: coat you apply. This serves to bond the two coats together.

That's not true if the underlying coat is fully cured, but there is some bonding between partially cured coats and new varnish. Cured varnish is chemically different from uncured varnish and it's impervious to the solvents that were used to thin it initially. Wipe a cured varnish surface with mineral spirits (the most common solvent in varnish) and it will have no effect (other than to clean the surface).

You also have to be careful about applying varnish coats in rapid succession, as you will end up with multiple "skin" layers that block oxygen from getting to the underlying layers, slowing the cure time even more. Rushing when varnishing actually results in it taking much more time to cure than if you allowed adequate time between coats.

: I usually suggest doing repairs and varnishing in the fall at the end of the
: paddling season. That way the varnish can harden over the winter storage.

Good idea. Time is your friend when it comes to varnishing.

: It is good stuff, so let it go longer and more of the solvents will work
: their way out.

The issue is actually oxygen working it's way INTO the varnish.

: Artists who use natural varnishes to protect their oil paintings frequently
: mix in a copal mixture or a material called Japan Dryer. These help the
: oils and resins polymerize a bit faster.

You need to be cautious, however, as many varnishes already contain dryers and adding more is not necessarily better. Japan Drier is is full of heavy metals and is highly toxic.

: Sometimes the best part of boatbuilding is the opportunities for relaxation.
: Drying varnish is Nature's way of saying: "Slow down". Take a
: few days off from building. Find an excuse to take the family out for a
: nice dinner, and tell them the boat is the reason for the adventure.
: They'll enjoy the boat even more after that.

That's a great attitude!