Yes, that helps! I consider this a large system, it's double what we have. Sounds like you use close to double the electricity we do, as our 8 kW system supplies 90% of our annual consumption. We're in central Oregon and heat mostly with propane and probably run the air conditioner a whole lot less than you do. I don't know if that $44k no battery quote is before any tax credits or other incentives are applied. If it's before incentives, it compares very favorably with what my cost was, but since my system is 10 years old, it's pretty much an apples-to-oranges comparison. Over those years, the cost of the panels has gone down a lot, and I assume the labor has gone up a lot. I actually have 2 separate systems. The one I'm using for comparison is 4 kW with Enphase microinverters. Its pre-incentive cost 10 years ago was $21k, so scaling that up to your 18 kW system would make the comparative cost about $94.5k, but as I said, somewhat apples-to-oranges.
My other 4 kW system has a battery. It naturally cost more, and I honestly don't know if it will ever hit financial breakeven. In spite of that, I am thrilled with the almost whole house UPS that it provides. When the grid glitches or goes down, the computers, TVs, most lights, and most 120 volt consumers keep going as if nothing happened. We often don't know the power is out until a neighbor calls to ask. Yes, the batteries are expensive. I don't know the going prices, but I do know the system-integrated Enphase batteries are very expensive. I don't know offhand what chemistry they are. Some of the "solar batteries" are lithium cobalt chemistry and I frankly would not want them anywhere near my house. I'm using lithium iron phosphate, which is much much less a fire hazard. Production-wise, the projection they gave you is very much in line with my production, with the 4 kW system producing about 6,000 kWh annually, but another poor comparison because of the geographic separation.