I believe you stated the problem in a way that its unsolvable. Charge your customers money, so you can work for them. I'm not nearly as certain as you are that Netscape failed because it was charging money. Netscape just stopped updating for multiple years at the height of the browser wars.
For Firefox in particular, I would 100% be willing to pay for it. Individuals like me who will pay are rare, but companies that will pay aren't. I think the answer for modern Mozilla is a Red Hat style model. Charge a reasonable amount of money. Accept that someone is going to immediately create a downstream fork. Don't fight that fork, just ignore it. Let the fork figure out its own future around the online services a modern browser wants to provide.
Then, lean hard into the enterprise world. Figure out what enterprise customers want. The answer to that is always for things to never, ever change and the ability to tightly control their users. That isn't fun code to write, but its profitable and doesn't run counter to Mozilla's mission. That keeps Mozilla stable and financially independent.
Mozilla will maintain lots of influence to push forward their mission, because hopefully their enterprise customer base is big, but also they are the ones actually doing the work to make the downstream fork possible.