In my experience, players are more likely to hiccup when they loop (seek) than when they are playing. To reduce the chance of seeing this hiccup, you deliver a longer stringout of back-to-back 10s loops. This was necessary in the olden days of DVD (to accommodate the drive's seek time), but it may still be a reasonable method today (depending on your player).
Since you have an odd number of frames, you could also implement Rick's interesting suggestion of matching your number of frames to the compression cadence by adding to a stringout, instead of going back to the drawing board.