So, first off, let me qualify my note above - I'm a big fan of GK amps, and have spent a ton of time with 700RBs. I've also damaged speakers with them, so you're in good company.

I've also learned from that experience!
Honestly, the 4/5 string button is probably the first thing to look at. It really does add a ton of low frequency energy to your signal in the most speaker-damaging regions, and it'll exacerbate any other low-end EQ boosts that you have further up-stream. As with any of the changes that have been suggested so far in this thread, you will absolutely notice a difference in tone if you switch to 4-string mode. You'll probably miss it (you low-end junkie, you

)! But over time you can wean yourself off of it.
With bass, and amp EQ, start with EQ at center and then try making small adjustments from there to taste. This could be another area where you might need to reprogram yourself a bit. Odds are given your taste you'll still probably wind up with bass boosted slightly on each, but hopefully overall EQ settings will end up dancing around center as opposed to settings boosted across the board. Tip - on your amp, try adding low-mids first before going straight to adjusting bass.
The last point that I'll make is about balance. Using the 5-string mode of your amp (as I do with mine) isn't inherently going to cause damage. Same with a bass boost here and there elsewhere in the chain. But put them all together, and add in low tunings, hard attacks, and loud volume, and you have a recipe for bad things to happen. Something has to give somewhere – it's just a matter of finding the right balance for your needs.
Last note, depending on how flexible you're willing to be on your tone, sometimes the only option is to add more cab so that individual speakers aren't being taxed as much to get the same amount of low end volume. Only you can determine which balance is right for you though. Good luck, and report back with your findings!