it's Elmo, and he refers to himself in the third person... i.e. "Tickle Me, Elmo" which could mean that the structure is not valid for all non-elmo subjects (most subjects) which is frunked up for me.
then again, he never says me, so maybe that demonstrates that the quote is not coming from him.

I then checked all the other season answer lists for the same format (lengths of each word in order) I could find just to make sure.
I'm not sure if I can brag about this work anywhere. LinkedIn maybe.
The solution was NOT Aardvark on Alabama and Albert.

I can't find a video of that episode online, but here is a screenshot from an episode 2 weeks later of what looks like the same woman with the same style of board (i assume they change the board and the hosts over the years)
Guess the "puzzle" in this screenshot:

I ran into the result "VISITING AN ANTIQUE CAR MUSEUM What Are You Doing? 11/15/16 #6482 R1" (not "Wax" museum).
That table row means: Episode 6482, Round 1, on 11/15/16 (american date format) which is a plausible lead.

Looking for sources I've found lists for each individual season with sources, and ran this regex ^\w{8}\W\w{2}\W\w{7}\W\w{3}\W\w{6}.*Doing.* on each one of those lists individually.

A list of answers with no sources gave me "Visiting an Antique Wax Museum". That's a possible answer for the letters, but I wanted to confirm that was actually the specific answer used in this episode.

It's controversial: on one side people are calling it "disgusting", on the other side some people haven't seen it.