Two things..........

An exhaust extension does wonders. There are ready made ones at the LHS or you can fashion your own. They'll show you where you should whack out some more wood. And it'd be very sensible to whack out that wood. It's dead simple and easy to do (if you have a few tools) and there are no rules that say you shouldn't. Matter of fact, I'm positive there is at least one rule that says you ought to. And any exhaust obstruction that's not plugging the exhaust is not really going to have much effect on the engine. Muffler pressure that's tapped out of the highest pressure area in a muffler isn't usually more than about 1psi, so anything thats outside the exhaust and is farther away than the diameter of the exhaust opening is going to have little effect.

And the other thing........ All the advice you've been given is good but....... What you described could also be a simple case of too lean. They'll shut off at half throttle when they're too lean just like they'll do when flatout. Did you see any exhaust trail? And when an engine is running on half-throttle, the lowspeed needle has some say in how it runs. Tuning the highspeed to lowspeed on some motors is not easy.