I'm seriously considering this one from Harbor Freight, which has lots of rave reviews. The price is right, only 10 pounds heavier than the Honda, half the price, very quiet at 63 db. Inverter Generator - 4.7HP, 2500W Inverter Generator
Now, I have bad lungs from asbestos exposure when I was a kid in the Navy. When the humidity is very high and and the nighttime temperatures are above 80, I find it difficult to sleep because of the difficulty in breathing. That's why I have a heat pump on the boat, but there is a lot of time that I'm not tied to the dock, so the genset will solve this problem. Additionally, I spend most of my time on the water during the week when I have those secluded anchorages to myself. More often than not, there are no other boats within miles of me, so that 63 db engine sound will not be bothering anyone other than myself. Inside the cabin, 63 db is barely noticeable.
A couple years ago, when I sailed down the ICW in October, it was one of the coldest on record. That heat pump would have been a God send to me if I had a genset back then.
As for charging the batteries, no worries - my 100-watt solar panel does a great job of keeping the 4 T-105s topped off, even on cloudy days. However, the genset would be a nice backup, if needed.
The only thing I will have to do is construct a platform on the transom to hold the genset and keep the exhaust fumes out of the cockpit and cabin. That's not a problem. In fact, I may construct a platform that has a cover so the genset can stay in place all the time, and it will also be out of the weather.
All the best,