I'm pretty sure the answer is no, but I figured I'd ask anyway. I'm planning on creating a pet in about 2 hours (because I want him to have January 24th as his birth date), and lo and behold - the zapper just zapped another one of my pets into a dang Common Experiment ... the same exact thing I was going to change this NEW pet into once I get him.

Is there any way I'm not thinking of that would allow me to swap the two's species/types that wouldn't involve my new pet having the other pet's birth date? I know you can swap names, but sadly that won't help me because of the whole January 24th issue. I hate that I'm likely going to have to find a different way to change him... it's frustrating. The one time I get a good, relevant zap, and it's two hours too soon 😡

No, just keep zapping or use experimental dews on the new pet until you get that experiment. You could also use miracle potion II to change into any species you want, but it's really expensive and only makes the most sense changing another angelic pet into an angelic neela.