Paging astronomers

For a plot point in a possible future Supergirl story I've been wondering about Krypton's moons. This page puts together information in the Superman comics etc. and makes some guesses about the moons as described there:

http://www.bigapricot.org/other/krypton.shtml

My feeling on this is that they're too close to the planet and to each other, and would either drift into tidal lock or end up catapulting each other out of orbit pretty quickly. I know that there are at least a couple of astronomers on my friends list, anyone able to crunch the numbers?

( screen shot from animated series )