Martin, I likely have the same generator. And I agree, it's a loud sucker. About 3 years ago I stoped by a muffler shop, bought a small car reverse flow muffler, 1 1/4" inlet/outlet and about 1' of pipe with a 45deg bend on one end that I welded to the outlet. Screwed a nipple into the head, used clamps and flex tubing to hook up to the inlet. Also welded a bracket up on the frame.
All the above made it is a small, make that small amount quiter. Seems the generator itself is a noisy (make that very noisy) generator. Lessen the engine exhaust noise and it's still very loud.
We horse camp so we always have hay on hand while camping. Best solution I found was to use 4 bales of hay, make a V two bales high and set the generator in the V with the open side facing away from camp. One time I used insulated foam panels to form a sound fense. Hay is better, the generator is much quiter with the hay barrier.
But the best solution has been the Hondia EU3000 we bought last year. It is expensive, but man it's nice.
One last hint on the Tecumche. If it's been sitting a while, turn it on it's side with the carb down for about a minute. Mine and my brothers with then start first pull of the cord.
Good luck, RR