@SteveThackery Thanks for your thoughts. I guess there does seem to be some cause for optimism. Hopefully, based on what I've seen, a low voltage situation in my case will cut voltage to the Arduino, which will also put the servos in hold mode which should be enough to bring the voltage back to above 4.5v again (which seems to be enough to unlock it).
Thanks for the suggestion of another battery. Unfortunately this might be a bit tricky due to size constraints. Similarly, not sure how much choice I have in terms of modules. This seems to be the only common one I've found so far.