Scuff-sand the washer with 400-grit paper so there's some "tooth" for the adhesive to engage, put a piece of adhesive tape on the bottom of the washer to seal the hole, then clip and file down the tab or integrated base off the figure in question. I like to leave a slight remnant of the base or tab between the feet - it increases the contact area for gluing.
Get about a dozen of each set up at once, then mix up a small batch of epoxy glue. Use a coffee stirrer or similar tab to lay down a sufficient amount of epoxy on the washer (filling in the hole at the same time, bed the figure's feet in the glue carefully and then use bits of Blu-Tack or modelling clay to support the figure until the epoxy dries. After the glue is dry, peel the adhesive tape off the bottom of the washers.
If you can only get the "5-minute" epoxy (which has a working time of about 2 minutes, actually), only do 5 or 6 at a time.
The epoxy is more resistant to shearing forces than most superglue bonds. If you plan to rebase figures ever, this technique should be avoided - in trying to remove the bases, the pewter or plastic will fail long before the glue will.
Apply sand or base modeling, then prime the figures and paint as normal.