Also, do you have any formulas that can go past 20 days?
Reducing yeast, or further increasing the recipe without increasing yeast as you're already planning. There is probably a practical limit to the length you can achieve. The most I usually hear about is a month. There was a guy trying for a three-month mix, but if I remember correctly, the reaction stopped prematurely after only a few days.
I recently heard adding a shrimp pellet will add a couple extra days before the yeast die. Just tried it in two 2L bottles with the following recipe:
1.25 cups sugar
1 tsp. baking soda
1 tsp. yeast
One bottle with a seafood wafer, one without (I don't have any shrimp pellets). The one without died completely yesterday. The one with is still producing at about 40% of desirable bubble rate. Nothing spectacular, but worth a seafood wafer I guess.
Other extension techniques are time-release sugar through the Jello method. Have heard of people getting a month or more. I haven't tried it; seems like for the extra work involved, you could just as easily mix a new batch.
And specialized yeasts. Champagne yeast is supposed to ferment more slowly and evenly, and be able to tolerate twice the alcohol content, so theoretically you could add twice the sugar and get more than twice the lifetime. Again, haven't tried it. Champagne yeast is more expensive and has a short shelf life, and I know of no local sources so I'd have to pay shipping too every few months.
But if you desire a long-lived DIY bottle enough that extra cost/effort is worth it, these are worth looking into.