Since I have a very similar system to what you are planning I though I'd share some of my experiences, and things learned the hard way along the way.
I see you've listed 14 awg wire from your 15 amp charger to your six volts. What is the distance of that circuit?
I am using about 2 feet of 10 awg on my 25 amp charger, before it reaches the 2 awg cable of the Perko battery switch.
This 10 awg cable gets hot with 25 amps and is still very warm when the charge tapers to 14 amps. Consider fatter cables from charger to batteries. I love having a battery monitor.
One thing to consider is that if your are parked in the sun, it's possible your battery charger will sense this solar voltage and not charge at anywhere near it's 15 amp rating.
If I want 25 amps out of my Schumacher "smart" charger in daytime, I need to pull the fuse on the solar panel. Together in sunlight, the output is usually less than just the solar itself.
Even though you have all week to recharge your 6 volts, you might find occasions where you wish you had more amps available. I know it's happened to me, and I have a 25 amp charger. I don't see how going over 15 amps on the charger complicates things. Your 120 volt system won't be taxed powering that charger or a significantly larger one, not even close, and all you need to do is fatten up the wires and fuse to the batteries.
My only provisions for 120 volt systems is a surge protector power strip and an extension cord. I rarely have anything plugged into the 800 watt inverter anymore, but If I need the battery charger, I plug that, my fridge and my computer into the power strip and connect to the grid. Maybe a dozen times a year. I don't really keep the charger mounted. Just have a quick connection to the Perko switch, and a couple flat bungees to hold it in place while it is in use.
My batteries also seem to like being occasionally blasted with a shorter duration higher amperage blast from the wall charger other than the relatively light amperage of the solar. Yours might too.
I find the output of my 130 amp alternator to be disappointing. If my monitor claims 60% SOC it will say the alternator at first is outputting 65+ amps. Within 5 minutes this number has fallen to around 12 amps. After an hour it is down to 7 or 8amps and would take 7+ hours of driving to bring the batteries back to 100%. I have shortened and thickened the cables from the alternator to the batteries, and blown a fusible link in the process, but have not significantly improved alternator output.
Your vehicle's charging system might be better or worse. Keep in mind it is not deigned to charge deep cycle batteries, just quickly replace the shallow quick discharge of starting the engine.
Depending on how your battery isolator operates, and/or is wired, you might be using your house batteries in addition to the starting battery when turning the key to start.
Once before I had solar, I'd forgotten to isolate the engine battery, and all 3 house batteries barely had enough juice to start the engine, and the ammeter on the dash swung up higher than I'd ever seen it, then swung flat. The newly rebuilt alternator's brushes had blew off the armature( I did not know this at the time) and I was stuck in Baja with 3 dead batteries,an inoperable charging system, miles from the nearest town with the warranty on the alternator redeemable north of the border.
After fully charging the house batteries from the grid, I was gonna make a run for the border. About 10 miles into the trip over washboarded road the brushes re connected and it started charging again.
After your first startup with depleted 6volt house batteries, check your alternator charging voltages, because the weakest link in your vehicles charging system will be exposed then. With a blown fusible link, or inline fuse, or a fried diode in the alternator and you'll be calling AAA on your first outting.
And for some reason, when My engine is running, the output of my solar panel usually falls to the 0.1 to 0.2 amp area, instead of adding to the alternator output, the controller seems to sense this output goes open circuit. Not always but usually.
Good luck, and have fun.