Sorry Smack but your post brought me to this old thread for the first time so of course I thought I would throw my 2 cents in.
First off, my 20 year old H376 has performed just fine for me. Many time I wished I had a heavier boat not for structural reasons but for the ride -- mostly in the Caribbean Sea where I was always reefed to at least half my sail rolled up so I would have been faster in a heavier boat. However, many times I have loved that I was in my Hunter sailing when others were motoring or staying in port complaining about no wind.
I would also like to add that I think I got a 'friday' boat. I should have known when I was the 5th owner in 9 years. The boat had a lot of manufacturing defects -- little things that made the boat noisy offshore down below like. This defects were mostly a lack of caulking where there should have been some between the deck liner and bulkheads. Another one was the L shaped galley cabinet was not bolted to the floor properly. Two others were a defect in the fiberglass of the deck liner causing it to rub on bulkheads.
As for structural, I am been very pleased with it. I have cruised on it from Texas to Fl to Bahamas to Colombia to Panama to Bahamas to Grenada to Panama and now Tonga. I will admit the worst I have sailed in is gusting to 37 knots apparent but am considering making the trip to NZ which almost guarantees 50-60 knots of wind for a day or more. There is already a sister boat down there now for sale so they can make it. My hesitancy isn't about the strength of the boat, but of the horror stories of those who have made the trip. A nice heavy blue water boat owner told me "Nothing to worry about. Just heave-to. The only problem is things tend to break in those conditions. We broke our chainplate" and I said "that is exactly why I don't want to make that trip"

I don't like rough sailing and I hate breaking things on my boat but I am still considering it, just so I can shut these people up. I am re-bedding all my port lights just in case I do decide to go. Doing the trip on 20 year old caulking doesn't sound like a wise decision, especially now that the caulking is starting to crack.
I have thought about moving up to a bigger boat and maybe someday when I can afford it I will. I am one of the smaller sized cruising boats in most anchorages and I could use some more space for a water maker, another person, more dive gear and a better insulated diesel generator. Cat seem to be catching ground on monohulls in the cruising anchorages with about 40% being cats and mostly fairly new so they must be outselling monohulls these days. Not sure about a cat though due to cost and hull slap issues. Thought about a newer and bigger Hunter but the swept back spreaders do drive me nuts at times when sailing so I'm still looking. Also think Hunters are bad at providing storage space which is very important for a cruising boat. I have plans to rip out the solon area and nav station and re-do it to provide more storage space on my boat.
So are the mid to large Hunters a great cruising boat, no. Is she capable, yes.
https://www.tradeaboat.co.nz/detail/hunter-376-338467