Best ways to make mainline browsers private?

Sorry for the little rant here, but I've spent years using every one of the high level alternative browsers. Vivaldi, Brave, Waterfox, Librewolf, Opera, Zen, Tor etc. And of course the mainline ones: Chrome and Firefox.

These days I'm primarily using Librewolf. But, lately, it seems like I'm having to switch over to proper Chrome or Firefox to get most of the websites I need to work properly and find that more often websites are just broken in it - navigation doesn't work, certain links that perform functions (ie not just HTML links) don't work, pages don't load properly. Etc. Usually, my first course of action is try the broken website in Waterfox, Vivaldi or Tor, and also trying them after disabling uBlock and the browsers built in blocking. Typically I find that the only browsers that the broken website operates properly in would be Chrome, Edge or Firefox. This makes me think it's a basic browser vs. website problem. (And the "theorist" in me is saying that this is not by accident. Websites with G Analytics (all of them?) etc probably are broken on purpose in non Chrome browsers, but I digress...)

And so I've come to the idea, that if I'm finding myself having to use proper Firefox (The only mainline browser I would really trust the "best".) to get the website to work half the time anyway, maybe it's better for me to use that and try and make it as private as possible? Outside of installing uBlock on Firefox - are there any holes that I can patch otherwise and not break websites?