Carbon fouling?????
You have got to be kidding me. Even my 6 hp Evinrude twin (2 stroke) can idle all season and not carbon foul. A four stroke normally has no trouble with that. But, with that said, I would check to make sure the choke is not sticking somehow in someway as this causes a really rich condition (easy check as you don't have to take anything apart except the cover). Then, I would check to see if they actually torqued the nuts (all of them, included the manifold it is bolted too) on the carb to see if they were loose as this will cause a vacuum leak and can cause the carb to go full rich in some cases.
With the simple stuff out the way and if you have still found nothing, it is time to check the float to see if it is sticking or set way too high (a float that is too high will cause a rich condition). Then, while you have the thing apart, you might as well clean it really well with intake cleaner and put a carb rebuild kit into it. Make sure you thoroughly clean all tubes and tiny passages or you will likely be doing it again. You will probably find the carb has some varnish, maybe some other gunk, and generally dirty if it wasn't stored correctly - sometimes even if they were.....God knows I have had my share of fuel system troubles over the years and I am pretty meticulous about how I store a motor in the off season.
I strongly suspect that the shop is right, the problem is in the carb. It is tough to tell what it was without a full dissasembly, and even then sometimes hard to tell what exactly was dirty as it doesn't take much crud to screw things up. You can replace it (normally the best, but hideously expensive), or try to clean it up and rebuild it. They are actually suprisingly simple in my opinion, but unless you are used to turning wrenches you may not want to tackle the job.
As others have noted, putting a new thermostat, hotter plugs, and checking the ignition system are all good things to do, but most likely if your engine is running really rich and carbon fouling, it is a fuel system problem. But is is alway good to cover all the bases - especially if they are easy
Good luck to you and let us know what you find.
Tim