Is there a simpler way to ensure that two inserters always fire at the same time?

Since they are so close, you could have a single requester chest feed a splitter

Your solution basically switches on both inserters, only when both boxes are filled with at least one frame.

You can do this easier by just directly wiring the inserters and chests crosswise (connect each inserter with the other inserter's source) and checking for "frames > 0".

If both chests have at least one frame, both inserters move. If only one of them contains a frame, the opposite inserter would move, but can't (because there is nothing to take).

This still does not help you with the stack size bonus, but at least you get rid of the inserters.