It's a tough call with refluxers. It sounds like he is ready for bigger bottles, or at least is hungrier now - has he started to get hungrier since he has started spitting up more? You could offer smaller feeds a bit more frequently - if he is on a 3 hour EASY you could drop it back to a 2.5/ 2.75 so he gets an extra bottle or two during the day. He is getting a good amount of formula over those 5 bottles so I wonder if the reflux meds are working well or is it time for a tweak?
My DD started pouring her thickened formula back up when she was about 4 months old, she would literally just open her mouth and it would flow out of her, so we had to start solids early at 17 weeks (under the guidance of her paed), rice cereal was a good move for her.
Laura