No shuttle, one time I did it I was able to get one of the Fedex drivers to take me over but Lyft/Uber is the only way across. Took a cab once and it was $20 from the terminal to cargo, you'll never get one to pick you up and take you back.....
That time of the morning there should be some ride share cars around, I wouldn't think your cutting it too close unless FedEx is late because the sort was late.