I recently fixed my bathtub handle valve stems (Repairing a leaky valve stem), and all of the leaks stopped - but a new issue came up.
Now, whenever I turn on either handle (hot or cold), the water coming out of that pipe will stop abruptly. For example, if I turn the hot handle for 2-3 rotations, the water will come rushing out, but after a couple of seconds there will be a thud and the water will stop coming out. This can happen on either the hot or the cold. I can then continue rotating the handle and the water will eventually resume. Currently, I avoid this by just turning the handle 6-8 rotations, but this is obviously an annoying problem. As far as I can tell, there are no leaks anywhere (even inside the wall).
For context, the valve stems were some very old Gerber stems (the house was built in the 1960s, and these are the original valves). I could not locate replacement valve stems, so I ended up taking them out and replacing the bonnet packing (sometimes called a packing washer), o-rings, seat washer, and seat washer screw on each. This problem did not occur before, but does occur now.
One possibility I've read about is an anti-scald mechanism, but this problem didn't occur before and also occurs on the cold side. Another possibility is a loose piece of sediment flowing up and jamming the valve, but it seems too coincidental that that issue would happen on both the hot and the cold valves, and I don't know why turning the handle more would resolve it.
What is causing this and how can I fix it?