I have struggled with my own volume issues, so I'm compelled to throw my bias into the mix.
Even a 12 watt amp can put out a LOT of sound, especially in small venues. My main amp is a Dr. Z MAZ Jr 2x10 combo (18 watts), which can be VERY loud on stage. I bought a Tonemaster Deluxe Reverb as a lighter option, but it is anemic compared to my Dr. Z.
A couple suggestions:
1. As others have stated, invest in a wireless system and get out into the room for a volume reality check. Wireless gizmos have never been cheaper, and certainly reliable enough for setting your overall volume. Defining a problem is the first step in fixing it.
2. While I like having my amp on the edge of break up, I am totally comfortable setting my volume to accommodate the venue, and adding an "always on" pedal that gives my guitars a bit of girth and sustain. I use a Greer Lightspeed pedal, set for very low overdrive, and it mimics the effect of my amps at the edge of breakup. You can also use a little bit of compression if you miss the perceived sustain of a turned up amp.
3. I believe the "beam" issue is more problematic in a small venue. The sound doesn't get to spread out, and patrons are much closer to your stage. Try some kind of baffle or plexi panel to attenuate the beaminess.
4. Don't point your amp at the sound man! Instead, use it as a stage monitor aimed at you, without disturbing the rest of the band. I find using my guitar amp as a monitor is more enjoyable because I can more accurately hear what I'm actually playing. If you do this, I'd bet that your sound person will (1) never complain about your level again, and (2) likely need to put your guitar into the PA.
5. Amp modeling and in-ear monitoring is becoming ubiquitous and some band and venues REQUIRE IT. I haven't gone that route, but I have heard bands pull it off extremely well. It may not be a solution for you, but it may be worth considering if you're on the fence.
Without witnessing your situation it's impossible to tell if your sound person is right, wrong, or maybe just not fond of electric guitar. I have run into sound techs who cripple the guitar levels at the get-go because they are tired of guitarists who, more often than not, are simply too loud. Ask your bandmates and reliable audience members for an honest evaluation of your stage volume. Is your sound person the ONLY person who has asked you to turn down, or has this been a trend you run into before? How often are you asked to turn up?
Good luck, and keep it fun!