Your best course of action is to drop chrome support, and make your extension as good as possible and make a point of marketing that it's firefox only. Most won't do it due to worrying about market share, but alas IMO it's the best option available
This is a great but only a temporary solution. Firefox is taking jabs at extensions not on its recommended list with slightly scary warnings.
Firefox as a privacy focused browser should give users the ability to limit permission or sites extension can run on - including click to run option.
Without this, they'll soon go the way of chrome.
Heck Chrome started locking down extensions when they started catering courting enterprises. And they included the ability to make extensions uninstallable.
Bad actors took advantage of it, forcing chrome to tighten things further until extensions could only be installed from the store.
I couldn't ask them to switch browsers for my little side project. I have to co-operate with Google's bureaucracy. For what it's worth, so far it seems like Mozilla is not exactly streets ahead, but at least they didn't charge me and they seem to be fairer and more helpful to extension developers (they have a "self-distribution" mode with relaxed oversight I used while in private alpha, and their tools and docs are better).
When Chrome was better, I suggested friends and family use Chrome. Now I think most people would benefit from using Firefox as their primary driver.
I think we as developers overestimate the resistance to switching.