Turns out Lee Meredith is so clever that her Either/Or mitten pattern not only works for any gauge, you don't even have to know your gauge before you start. So I didn't swatch after all, but just cast on the top of the thumb.
(Check it out, I just found a knitter blogging a whole year of mittens! She's doing the Either Or right now, too, so it will be cool to see how that turns out.)
One thing you'll notice if you try this pattern, or any other that allows for a variety of gauges, is that the rate of increases is generally what matters, not the number of increases. Let me say that again.
The increase/decrease rate stays the same no matter what your gauge.
This means that if you're adjusting a pattern to use a different gauge, you probably don't need to do much with row counts (Knittrick gives you the option, though!). For instance, a sweater pattern might tell you to cast on 20 sts for the sleeve cuff and then increase two stitches every 6 rows for 60 rows.
You might think (I would sympathize) that you need to figure how many of your rows equal 6 of the pattern's rows, and then do your increases every 5 (let's say that's what it worked out to) rows instead of every 6. NOOOOO!!!!! DON'T DO IT!!!!!!!
If you did that, you'd end up adding the same number of stitches to the sleeve as were added in the original pattern. But your stitches aren't the same size as the stitches in the original pattern, so you'd be getting a sleeve that's, say 12" wider at the top than at the cuff instead of one that's 8" wider. That's bad.
Instead, you can just happily increase two stitches every 6 rows, just like the pattern says. The difference is, you won't be doing this for 60 rows. You can convert that overall row number, if you want, but it's probably best to work from the stitch counts. In our hypothetical pattern, maybe it's super helpful and puts a little "(40 sts)" notice right after the part where it tells you to repeat the 6 rows for 60 rows, to tell you that you'll have 40 sts when you're done with all that. Or maybe you have to figure out for yourself that the pattern is doing 60/6 = 10 increase rounds, which each add 2 sts, so you'd be adding 20 sts.
Either way, you can fire up Knittrick and tap 40 into the Adjust a Pattern screen, and you'll find out how many stitches you need at the top of the sleeve. So, knit your sleeve, increasing every 6 rounds, until you have that number of stitches. See?