That's a great idea, thanks!

A quick update: The stalks and leaves have grown huge and definitely look fine: I hope there is also something happening below the surface.. :) I'll let it grow one more month and will dig them up in September. Hope to get at least a few tubers!

You will get the best yield if you let the plants grow as long as possible. I often have many TPS plants that grow until past the first frost, some even until the first hard frost. If the stems are still green and growing, then tubers are still growing.

The results for this project: a couple of tiny nobs that I will save until next spring, and plant as seeds for the new crops :)
So, not a total waste! I know potato tubers are very eager to sprout, so next year I'll get to taste this variety. Hopefully.

Continuation 2018:

Sadly, no crop. I planted tiny seed tubers and they begun to grow well, but probably got too crowded in the bucket. Also they were unfortunate enough to get a ton of water dumped on them from the roof during a storm... The contents were all rotten. I am not defeated though, will try again - even if it's a strenous process!
My other potatoes from grocery store tubers seem to thrive... Another month to go.