I wanted to update this thread in case someone else runs into the same issue in the future. I installed the MOVs that geostep aka George suggested (thanks George!) and they work great. The meter seems to still be in spec, at least for the ranges I can test on my bench.
One thing to note is that while the MOVs to be replaced were "about 10mm" and the replacement was "about 10mm" the replacements were actually a bit larger. The old ones were 8mm at their widest, and the new ones were 13mm at their widest. It turns out this matters in terms of fitting them in the case.
Being impatient, I solved the problem with a Dremel on one of the internal plastic layers. Not ideal, I know, but the meter is working great!
Thanks again to all for your help.