I use floortime as a weekly change of scene for my piggies, as I completely clean out their cage (which is huge - so the floor time isn't such an issue). How big is Gideon's cage? I agree that he feels secure in his cage, and is frightened by this expanse of space.
Give it time. As STTW suggests - give him AT LEAST an hour. If you give him his veggies in the morning, set up floortime, than spread the veggies around the space, so he has to explore to find them.
If you have the time to spare, get in there with him, and be there for reassurance! Or make the floortime completely secure (cable tied grids make a super enclosure) - if you have other pets, keep the door closed - and let him come out in his own time. You could let him stay in there for a day. I sometimes leave my 4 girls in their floortime space (whole bathroom or larg enclosure) overnight too. As soon as they're put into their weekly floortime space - they are out and about exploring! If a long time is out of the question, then make it a regular daily activity if you can.
Another piggy pal would be the very best thing to help him enjoy floor-time. I'm sure you're aware that the best toy for a piggy is another piggy!!