So, let me get this straight.
Dealer and other repair shop wants $3000+ to fix it for a $1500 part and $1500 labor.
A shop says they can do what you described as "cleaning" for $300. $300 later, problem not fixed and you go over and described in detail what needs to be done, as well as showing them exactly what to do, and $1000 later, issue you want them to fix is fixed.
Dude, this totally is on you. $300 would be way too cheap on the "cleaning" job and you knew it. How do I know? You said the cleaning will take 10 hours do it, any shop I know of charge $70 + / hr, and at $300, the job is way too cheap. You probably were too happy to ask why it is so cheap compare to the $1500 quoted labor for replacing the intake manifold.
And you actually saved $200 on labor, not to mentioned don't have to buy a new intake manifold.