I talked to a co-worker and he led me to an idea - I might simply add a period button in the bottom-right corner of my "page" (and somehow explain to my users why it's there and let them disable it in options).
I was thinking about somehow preventing the regular keyboard from popping out and writing my own, but I feel like it's an overkill to solve such a "small" problem.
As for the ","/"." issue, we also use "," in Poland... it's not a problem, I just assume people are smart enough to figure out that they need to use the period character. Similarly, I've had (considerably more) complaints from Korean users who would like to separate every third zero with a comma (1,000,000).