I think maybe you have two problems. Either it's a HF volt meter or the battery in it needs replaced. I get radical readings in my American Made Fluke multi-meter when the internal battery gets low.
If you have unrestricted fuel to the pump and it doesn't pump, even though it runs, under "working resistance" to the motor it doesn't move fuel you may need a new fuel pump. Have you tried a pressure gauge at the outlet of the pump??. They're fairly reasonably priced at your parts store. They are a low pressure/vacuum gauge.. .Just some rambling thoughts....Maybe don't mean much....
Be sure to let us know your fix...
PS.. What I don't understand is how you can get 20-35V out of a 12V system. If that is possible then I should expect a 24 pk of Bud the next time I buy an eighteen pak. How do I 'splain that to the check-out gal?? :)