The blue rug remains the focus of our training so far, and we're still working on a making it a place he will want to go on and thus make it a very attractive place for him to go to.
We worked more on shaping and then just getting the spot being a trigger for a reward even when not making it an explicit target of training. If he walks on it during the day, he gets a click and treat. If he walks on it while playing, I'll praise and give him a treat. If he lays on it, sits on it, plays on it, whatever, he gets rewarded.
I think doing that - getting him rewarded for being on, or stepping on, the rug is a good first step to getting him to offer it on his own during shaping. I've done something similar before - teach him a behavior outside of shaping, then have him refine, master, and fully reinforce the behavior during shaping and games.
Also found the Spanish word that I'll link to the rug, 'tapete'. Then I'll use "¿Dònde està tapete?" to tell him to find the rug.
That is the first "formal" game we'll play with the rug.
The other side effect of this is he'll get more "mat work" as well. The things learned here could carry over to that exercise as well, since the concept is the same idea: get to the spot where the "mat" is.
So that's where we are with the rug and our continuing practice in working with it.