Least Shoddy Fuel Sending Unit?

The 7805 regulators that I used to build the demon IVR would start cold at about 4.9V but as it warmed up output would climb as high as 5.4V .
Oh? In the electronics world, that would be considered out of tolerance and would be pitched in the garbage. You might consider replacing it.
My 7806 regulators would start at exactly 6 volts and would heat up and be at 6 volts. I bench tested it under load for about a week before installing in my car. Then I made a spare just in case.