Oh boy, that's the lab coming through. This is a hard behavior to train for specifically because like you said, there's not a lot you can do that will motivate her more than the ball she already has (other than another ball like you have been doing, but that defeats the point).
Is she motivated by any other types of play or attention? Tug maybe? A toy she chews on? Or being scratched in a particular place? Is there anything else that she really loves? If so, I encourage you to get creative with your rewards for trick training. A bit of tug can absolutely be a reward for a command well executed. Scritches behind the ear and lots of praise work wonders for some dogs. Try some things out with less ... high stakes (for her) commands and see if you can teach her one or two new things with a variety of rewards that aren't food-based. If that works, then teaching her to drop it might be possible.
If she's really just not into any reward except the ball, then that's what you can use. Your system of "throw one ball and she'll drop the previous one" is brilliant, but you should stop using it. In situations that aren't with a ball, teach her the command Drop It. Food actually might be a good place to start, if she doesn't particularly care about it much of the time. You can also use toys that she's less attached to, household items, whatever. Take her outside, offer her something, and then ask her to drop it (offer the ball in exchange). When she does, she gets the ball and you have your playtime for the day.
When she's good at that, start keeping the ball hidden, or flashing that you have it if she needs a hint. She still gets it as soon as the thing is dropped. Make sure to practice this anywhere you might want her to use this skill - your yard, a park, indoors if applicable.
Once she's consistently dropping other items, start asking her to drop the previous ball before you throw the next one. Again, make sure she knows you have it and are going to give it to her, spend some time just practicing swapping them out without throwing too. She gives a ball, she gets a ball and lots of praise along with it. Eventually, she'll learn the new rule of "My human's cue to give/throw a new ball is to drop this one"
(Warning, this is a moment where some smart dogs say "Oh, my human's cue to give/throw a ball is to drop an item" and start stealing and bringing you random things (tv remotes, shoes, wallets, a roast from the counter...). It can be very cute but you shouldn't reward it unless you wanted her to do the behavior.
With the new swap system, you should be able to end playtime more easily and without the risk of fingers clashing with teeth. Make sure that every time you go inside, you still make it a very pleasant experience with attention and love and any other toys she enjoys.
