I could just multiply each value by 1.0/0.82292456 and then have the sum be 1.00, but then all values would receive a factor adjustment of the same proportion (i.e 0.17707544).
OK, That's what I'd do. Why is "a factor adjustment of the same proportion" a problem?
I'd like to increase each value based on the size of the value itself.
In that case, you should multiply each value by 1.0/0.82292456 because that's what multiplication does.