I don't recommend giving rice in a bottle. First of all, rice cereal is essentially empty calories. so when you do that you're replacing hte nutrients baby needs from the formula with rice cereal. It can also be a choking hazard. The AAP doesn't recommend it either.
It is generally better if you let babies regulate their intake just like they would if they were breastfeeding so if he's letting you know that taking the bottle away doesn't make him happy, he probably wants more. What you're feeding him doesn't seem out of the ordinary for his age either.
Will he take a different type of nipple? Maybe he's just getting the milk a little too fast? Definitely mention it to your pedi at your next visit. . .while GERD is one option there are other possibilities too. My dd spit up and did not have GERD. . .she just spit.

There was a reason but we didn't find out until forever.