I've got a late nineties Twin on long term loan at the mo and it ticks all the boxes you said. Very good thick bassy 'plummy' overdrive when pushed a bit...and with the 25 watt mode it breaks up relatively early, although still at some volume. It's no 'house' amp!
Main reason for posting though is because I've tried a newish 'The Twin' and a Matamp King Street side by side. I'm a fan of Matamp (I've got a Chino) but the Twin just blew it out of the water. It made the KS sound flat, honky and with no depth, and the KS is a pretty good amp. To be slightly fair this was at relatively low volume, but having a Chino, which shares the KS power stage, I'd say even flat out it would struggle. My Chino sounds very good indeed with my Les Paul copy though, probably because the preamp doesn't impart a great deal of character, which the LP compensates for.
The second reason for posting was because I had to buy some new power valves for the Twin a couple of weeks ago, and I just thought it was extremely unbelievably weird that out of hundreds of 6L6s, I chose NOS Philips JAN 6L6WGBs, which is what Fourth Feline put in his Laney. Weird.
To sum up at last - I'd never considered a Twin before because it's such an obvious, non boutique choice...but I tell you there's a very good reason they're an industry standard!!