all of my songs are 2xLSDJ 
you can use a modded 4-player adapter to keep 4 gameboys synced or you can just beatmatch them manually! it's honestly not that hard to hit start on both sets at the same time I swear.
every show I play now is basically a DJ set of my songs, so that means beatmatching! I run 4 gameboys into a 4 channel DJ mixer and monitor the mix using the pre-fader buttons. if you know anything about DJing then keeping 4 gameboys in sync is really not that difficult.
the basic show workflow goes:
1. start song 1
2. while song 1 is playing, load up song 2
3. when I get a chance, hit start on song 2 on time with phrase
4. put on headphones and monitor mix -- if song 2 is too fast, lower BPM a little until synced and vice versa
5. when song 1 is coming to a close (meaning just leads and kick), bring in lead from song 2
6. when song 2's main melody comes in, cut song 1
and then rinse and repeat for every song in the set!
it's a lot of fun and once you're good at it you can pretty much not talk for the entire set if needed 