Thanks everyone!
This response from a thread in the After Effects forum solved the issue and I’m good to go now–
“From your description, it sounds like you rendered out a high-quality HD file. I’ll guess it’s the Animation codec, best quality. Good for you.
Now to make it play smoothly in FCP, I’d simply Export the file from Quicktime Pro — which comes with FCP — in the codec you use in your FCP edit timeline.
Dave LaRonde
Sr. Promotion Producer
KCRG-TV (ABC) Cedar Rapids, IA”
Just exporting from QT made it play smoothly. Thank you for all your quick responses!