Excellent news!
It was the Comet Cougar alright!
Considering the possibility that the beach game may work for a limited time only, it may effectively be a "limited animal" after all, so I guess this is the best outcome of the three possibilities.
It's safe and sound on the nest now. I put in another breeding with the same animals and got a Rainguin; bummer that it leaves a useless 12 hour gap, but well, the night is part of that gap, so I'll just sit it out...