I couldnt find a good pic for an example, but imagine emptying the food hopper that you have built into the lid, and just sliding the water bottle down into it. That way, the bottle is able to be taken in and out from the outside, but the stem can go through the hopper.

Since you still need food, you either make another hopper or make yours bigger and add a divider.

This didnt seem to help much so I will try to find a pic.