AK to Saratoga Springs is fastest, if you don't mind walking from the Congress Park station to DTD. It's about a half mile walk to the Rainforest Cafe area; T-Rex might be 1/4 mile farther. Allow 50 minutes + walking time.
AKL is probably your best transfer point in the afternoon if you don't want to walk. Although it's slightly longer than some other routes, you'll avoid stopping at BB on the way, and there are no intermediate resort stops (you'll transfer at the Kidani Village stop at AKL, which is the first stop out of AK and the last stop for the DTD bus.) Allow 90 minutes if the weather is nice. If it looks like rain, the DTD buses may get delayed by a TL rain exit, so allow 20 minutes more. 3:00 should be plenty safe.
At DTD, there are 2 stops: Marketplace and Pleasure Island. PI is a little bit closer to T-Rex, but the walk is across a big parking lot, and it takes 5-10 minutes longer for the bus to get there. It's probably just as fast to get off at Marketplace, and enjoy the walk through the heart of the shops.