What I do may or may not work for you.

First, I have never had luck with a Gore-tex boot. It seems that I rarely need the waterproof feature and by the time I do, the membrane has failed from regular use. And in the meantime they are hot and sweaty in dry conditions. So I only use non waterproof boots combined with Sealskinz socks when needed. This worked reasonably well with a pair of leather boots. I just can't use a regular hiking sock inside the Sealskinz. Makes the boots fit too tight.

I have since switched to a ventilated type boot with mesh upper. Haven't had a chance to hike with them in really wet conditions, though. But I expect they will provide the advantage of drying faster than a leather boot.

One thing I've learned that helps dry a boot overnight in camp is to hang them upside down on a stick. That lets any water drain out of the boot instead of collecting in the insole.