I'd suggest an early start to do the safari. The animals will be more active if it's during a warm time of year early in the day. Last June, we did the safari right at opening. Just to give you an idea on what the timing might be like, we went from there to Kali and rode it twice (still early so lines were short). We also did Dinosaur, Triceratop Spin, visited some gift shops, had some lunch, then Festival of the Lion King. Visited the Rainforest Cafe gift shop and were on the bus for our hotel by 2pm at the latest. So, IMO you would definitely have plenty of time to get in some down time and head over to Epcot for some late afternoon/evening touring and Illuminations.
My only concern would be the possibility of arriving at Epcot midafternoon and finding that all of Soarin's fastpasses for the day are already gone. You could still ride it, but your wait would then probably be excessive.