Update: I rewrote this, as it's apparently been this way for a while and I found a way to make Firefox notice a local maxVersion increase.
When a Firefox extension is installed, the browser checks the maxVersion setting in an extension's install.rdf file. If it's incompatible with this browser version, the browser then checks addons.mozilla.org to see if the extension is compatible with this version of Firefox, which overrides a lower maxVersion setting in install.rdf.
This means developers don't have to upload a new version of the extension in order to increase the maxVersion, they can edit it in the Developer Tools section of AMO (follow the 'Latest Version' link and change the maxVersion in the drop-down menu next to each target application).
To make an extension that's already installed compatible, it seems to be sufficient to edit the install.rdf file and delete extensions.cache. Alternatively, manually disable compatibility checking for all extensions.