I agree that, given the current you measured with the scope and the 2.5A stall of the similar servos you found, the load of your servos is just too much for the regulator given your input voltage. If you are seeing 1.6-2A draws on just one of your servos, it seems unlikely to me that you would be able to power two servos off the regulator even with a steady 5V source. The efficiency curves of the regulators show data out to the maximum current possible for a few seconds, and the maximum continuous current output is typically at least a few hundred milliamps lower. For the U3V50ALV regulator with 5V in and 6V out, I would expect to get around a little over 2.5A continuously.
Unfortunately, we do not have any higher power regulators that would work for you and we do not recommend paralleling regulators. If you are interested, this thread has more details on the issues with it. If you are able to figure out the issue with your input voltage dropping, you might consider powering each servo off of separate U3V50ALV regulators.
-Claire