Thank you all for your input!

I've ordered a package of ID44 PCF7935AA transponders because the folks at keyecu.com said these only use ID44 chips. I came across a picture of someone holding it vertically in the programmer instead of a video I saw where they simply laid it in the bottom. So I can try various orientations to see what works.

I'll post an update in a couple of weeks (because they are coming from China).