How to free the rest of the web from advertising is not Mozilla's problem. They are not even asking the right questions.
As for how they should deal with finances, in my opinion they should've taken some of the many hundreds millions of dollars they're paid annually in excess of what it costs to maintain a web browser, and used that money to build up an endowment that would suffice to keep them funded for eternity. Mozilla Corp is said to be organized as a for-profit corporation in order to give it freedom from the legal restrictions that govern how non-profits can spend their money, so I don't see why it wouldn't be allowed to do that.
There are of course many other possible ideas. Trying to collect data about Firefox users in order to better target ads at them — while preserving everyone's privacy of course — is fairly close to the worst one I can think of. It thoroughly undermines their brand identity, and will only accelerate the loss of market share. Not being an ad company has until recently been the number one advantage they had over the competition, and they're slowly throwing it away piece by piece. Aside from the considerable technical challenges in actually doing privacy-preserving surveillance advertising, saying "we'll collect data about you for advertising purposes but never invade your privacy" is also practically impossible to convince people of. Nobody without an MBA is buying it, and I don't blame them.