No, it seems to be better when heat soaked, if it's just warm 5-10 miles it's pretty noisy, to me, but then I have had it since it had 7 miles on it, so I can really tell how different it has become.The documentation for the Lemon Law prosecution must show a dealer performed the evaluation. I would be straightforward in taking the video and explain the purpose is for LL. The independent shop can be useful as an "expert witness" who will listen to the engine and render his opinion. Capture this all on tape. It is not too early to bone up on the LL in your State. You only have so many months.
Sometimes the owner has car rental insurance for the purposes of loaner cars. Maybe it will work for the overnight exam.
I am still trying wrap my head around the need for the overnight. Didn't the OP say the noise is only when the engine is heat soaked?