You're not in the audience area. The FOH person is. That person is the boss - if he or she says you're too loud, you are. Arguing that point will get you nowhere. OK, it will get you "somewhere" - it will get your band fired from the gig. Is that what you want?
The PA/gain structure thing is a secondary issue - if you're too loud from your amp, there is no need to put you in the PA, whatever is happening there is meaningless unless and until you get your rig set up properly. You need to get your volume under control (and still hear yourself). After that problem is fixed, the issues with the PA can be addressed, but first things first.
The first thing you need to do is point your cabinet at your ears, not the back of your knees. This will fix a lot of things. Once your ears are in the beam of your rig, you will hear yourself much better, and will be able to back off the volume. You will probably need a stand that angles the thing, and yes, your amp head will not be on top of your cabinet once it's angled, but this is a necessary step in resolving your issue.
Whenever I've run into the "You're too loud / No, I'm not" scenario, this has been at least part of the problem - usually , it's all of it. It happens with bass, it happens with guitar - we share a common problem, in that our amps are designed to play to the audience, not to us. Nowadays, we have PA's, so our amps
should be designed like monitors, but they aren't. If you want to be employable, understanding and fixing the problem yourself will help. A LOT. A band thats "easy to work with" gets re-hired constantly. A band that argues with the FOH person about volumes does not.
Here's a speaker stand I made - it can angle at 35 or 55 degrees by turning the thing around. I used to play a "coffee house" vibe gig, and I needed to hear myself without putting out much volume - there was a harp (the 7 foot tall variety, not a harmonica) that I needed to work with, and me being too loud would destroy the magic of that instrument. I actually put my speaker in front of me, not behind, so it was facing away from the audience, but right at my ears. Worked great - everyone was happy. You need something like this. If you have two cabinets, you need two of these.
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