Including the browser itself by your words ("anything")... why we are installing it in the program directory by default then? (if you are saying that the browser may unexpectedly clobber it's own directory, that is fine but a really strange behaviour. I have tested creating the plugins location under the browser folder and unfortunately the browser didn't find the plugin, probably a change in Pale Moon vs Firefox.
Moonbat solution should have worked, and if this is one of the browser changes that was done to prevent this, and you knew about it (seems like you do based on your claims), you could have politely told about the new correct location in this case. (I couldn't find an official Moonchild post or any information about this (there were some discussions for Linux but nothing for Windows AFAIK))
During my search i have found a solution that is working for Pale Moon and opens pdf's in browser (for me at least). [edit: unfortunately is only per profile based with unknown system location for the browser]
1. You need to download the correct plugins folder for your current Pale Moon architecture 32/64 bit.
2. Rename the folder to "plugins" (without quotes)
3. Find your current Pale Moon profile. Usually under C:\Users\USERNAME\AppData\Roaming\Moonchild Productions\Pale Moon\Profiles\RANDOM NUMBERS AND LETTERS
4. Paste the plugins folder under the Pale Moon profile directory
5. Start/Restart the browser
6. In about:addons under plugins check that SumatraPDF Browser Plugin has appeared (it will only appear/work under your current profile since it is installed inside your profile directly)
7. Check that the plugin is set as always enabled, if it set as on demand and you directly open a pdf file/page you may see a white screen and would need to allow the plugin via permissions or other methods.