New instrument cluster

These instruments were originally designed to operate on 6 volt systems and that never changed.
The little 12 volt to 5 volt regulator that everyone used ( including myself ) was employed only because there wasn't a similar 12 volt to 6 volt package available. What we used would light up at 4.92 and slowly climb to approx' 5.3 as it heated up but... with 3 instruments drawing on that mere 1.5 amps, they would climb extremely slow and read slightly low ( not as bad in the more common 2 instrument setups ). There are adjustable regulator packages available and affordable today. Those should include wire leads long enough to mount it where its accessible for adjusting in the vehicle though. Therefore I wont state what is the best route.
The main thing you need to know, IF your 3 post fuel gauge does work, and reasonably accurate, you don't need to open it ( "bend the little thingy" ) to disable the mechanical limiter inside. All you need to do is lift it and isolate it from ground. Remove the slither of metal from its back side and replace it with a non conductive slither, or simply cover the general area with a couple layers of electric tape.
If you were to lift your 2 post gauges you would see those were/are isolated from ground ( this applies to every application/example ). Logically defines why a 3 post gauge ( limiter inside ) had to be linked to chassis ground.
Real Time Engineering ? More like Reel Time as in gone fishing in this case? They created a feckin' mess ? Maybe not. Consider the following...
The fuel gauge has worked hard at every switch cycle, for about 50 years. The more fuel onboard, the more heat and subsequent needle movement.
Those who do open the fuel gauge typically find a fat, crunchy, black casement of carbon built up on the winding and the bi metal beam bowed at room temperature. It simply cannot function like new in this condition. This instrument needed renew before reinstall so opening it turned out to be a good move.
I cant testify that this is why a vendor published the "bend the thingy" procedure.
I can testify that I opened 353 of these fuel gauges over a 8 year period. Majority of those ( about 90% ) were fried inside. About 40% of the oil gauges were fried. About 10% of temp gauges were fried too. Shorting a sender wire to ground will fry one just as easy as a faulty mechanical limiter. That happened more often that you might think with the engine mounted senders.
So... heat, age, duty cycles aren't the only factors, just the prominent factors for fuel gauges.
Back to your question and bottom line... Power source change will not be a cure all. Do it all or don't do anything.