I haven't had time to read the entire thread, so apologies if any repetition. I've got the HY3200sei and for its size it is both fairly light and reasonably quiet. A major issue is there is no way to secure it, so more suitable for a mooring. The actual output is 2.8kva.
I'm quite impressed by the Champion Atom fusion, and this may be an option, at around the same output and again, not likely to induce a hernia when moved. Whatever you choose, make sure it is an inverter type as most modern chargers won't recognise the crude, non sine wave power that 'site'type generators produce.