Man....my opinion? If you have the cash to add a powered sub to the PA, I feel as though that would be a much better investment for the band's sake than a bass amp or cab.
There are other options that people have stated above, but I think that having a capable PA system beats everything hands down. If you're gigging on the regular you'll get a lot more use out of powered subs (you can run bass through them, kick through them, full mix through subs and tops assuming the tops you have are good) than any instrument amp or satellite cab. As you stated, you could get something like the Pod GO (or another modeler) or even a good DI and be set, and use your amp for monitoring instead of FOH sound. It's modular - for smaller gigs, ditch the sub and use the tops; for larger ones, bring the sub.
If buying a sub isn't an option for you, then sure - try the highpass, the amp elevation, etc. It's all sound advice and makes sense. But if you were set on buying another amp specifically to address this situation - buy the sub instead.
My two cents.