Super Heavyweight Biker keeps destroying Dutch bikes
My experience is with load bikes rather than people who are loads, but the principle is the same. A tandem rated wheel is your best bet, and possibly a heavier frame. Unfortunately most Dutch bikes are built for tall Dutch people who are generally not that heavy. 370 pounds is about 170kg, which is heavy. Pacific Island rugby player heavy.

What I would do is another custom wheel for your current bike, but with everything focussed on the weight. You can get hubs that are rated to a lot of weight, and Rohloff for example rate their hubs for tandem use even with only 32 spokes. But you should try for more spokes, I think, like the DT Swiss 540 Tandem with 36 or 40 spokes, or if your bike will take it the Halo Dozen with 12mm axle. Pair that with a heavy eyeletted rim like the Velocity Chukker or Mavic 719 and get it put together by someone who builds a lot of wheels.

Getting a custom wheel built with exact components can be mildly annoying, and not necessarily cheaper or better than finding a decent bike shop and letting them recommend something for you. That way you get their warranty. I suggest a load bike shop like Practical Cycles (found via google, I've never been there or to any part of the UK). If you do that and they get it wrong, it's on them to fix it. The magic words are 


  fit for purpose  The goods should be fit for the purpose they are
  supplied for, as well as any specific purpose you made known to the
  retailer before you agreed to buy the goods.


(italics mine) Which incidentally means you should be able to get a complete refund for your current wheel if they can't fix it.

When we had this problem with a customer at the bike shop I worked at we first re-tensioned their existing wheel, but it broke more spokes the same day he got the bike back. Luckily he came back, because we were at least the third bike shop he'd been to, and even though I said "look, this probably won't work but I think it's worth trying" I wouldn't have been surprised to have him disappear. So we put together the heaviest duty rear wheel we could find, a downhill MTB hub we had in the shop with a 36 hole Chukker and somewhat oversize spokes (3mm straight gauge instead of butted just so it looked stronger). When I built it I took extra time to get it exactly right, and ran over it again after a test ride. He rang a few months later to say he hadn't had any more problems and just wanted to tell us.

(editing in some comments)

My feeling is that you can spend a lot of time and money trying to avoid just paying for something that will work. 

The derailleur wheel is dished it's not as strong, as Rohloff discuss here and this Rohloff fan page might help :).

Use a 26" wheel in whatever frame you have as you will be using disk brakes so it's easy. A slightly smaller wheel is slightly stronger. Also, look closely at the rear wheel of this thing. That's a 9 speed 20"/406 wheel with 36 spokes that I threw together the night before I left on that ride. Normally it had four large panniers plus stuff on the rack, but a band is more interesting to look at. It was still going strong several years later when it was stolen. Smaller wheels make everything easier. If I could suggest a 406 wheel bike for you I would