I find just pinning the tab (right-click on tab, select Pin Tab) on Firefox does what I need it to do. I mention this because I suspect many people are unaware the feature exists.

Pinning a tab gives it permanent priority on the left-hand side of the tab list, and elides the title from the tab, so it is just the favicon. It also blocks CTRL-w from closing the tab; you have to actually right-click and either unpin or close the tab. That may sound trivial, but was the biggest problem I had running it in the browser before, it got caught in my periodic tab cleanups accidentally. Now I never accidentally close it.