Do it all in 6/8, using dotted quarter for quarter, dotted eighth for eighth etc. this will get it to play (and align) properly.

If it has to look right too, copy what you have done to another staff group.
Then, in the "2/4" sections:

Put a visible 2/4 followed by a hidden 6/8.
Replace each of dotted notes with an visible note and hidden rest.  Replace each of dotted rests with an visible rest and hidden rest. Think of it this way, you have to hide 1/3 of it. trick is to hide the right third.

so true

I agree that it's sort of a pain you can't have compound time in one staff against simple in another. The easiest way to get it to sound right is to write everything in 2/4 and use triplets for the compound-time parts. But sometimes 2/4 against 6/8, or 4/4 against 12/8 or whatever, is easiest to read.

I think the easist workaround is to write everything in 6/8 as Rick G said, using a visible 2/4 followed by an invisible 6/8, but I'd fill up the 2/4 beats with invisible eigth-note rests. With the last revision, you can put an invisible rest between two beamed eighths, which makes it possible.

At a slow or medium tempo, it may sound a bit choppy, that's the only thing. If you really need it to sound exactly right, you can mute that staff and have a playing staff written out in 6/8, with duplets as dotted eighths and sixteenths and so on.