FFS, why don't people here listen/read the answers to their question!
Are you after the one person that will say Yes? Even at best you have been told it would be unwise.
Tell you what controller, go flying and if your calcs go wrong and you end up having to rush a landing before planning on doing so, just say in the report that the gauge failed in flight with the flame out happening while you were looking for somewhere to land as soon as practicable in order to check the tank contents. ( Assuming of course that no one is likely to investigate the circumstances that a. Reads PPRuNe or/and b. Knows who you are.)
Looking at your initial post, I wonder how long this guage has been u/s and how many flights it has had with it u/s.
The best indicator of whether or not you should take it up, would be to ask the passenger ( non fare paying
) if they would be happy to fly with you without a working fuel guage! CRM and all that ;-)
I like B.U.D.G.I.E.s analogy, you probably would make the car trip to Scotland, but it would be the most uncomfortable and stressful trip you could possibly undertake.