We could imagine that halfradians (the ratio of arc length to diameter) might also be a natural unit, and then we'd have to go into calculus to make a case for radians

I was actually thinking of diameter-radians when I wrote that, but I didn't know what they were called, so somehow I didn't make up a name. Thanks.

For utilities, we have two degrees of freedom. One way to convert such a quantity to a dimensionless one is to take (U1 - U2)/(U1 - U3), a dimensionless function of three utilities.

This is more or less what you're doing in your "dimensionless utility" section. But it's important to remember that it's a function of three arguments: 0.999 is the value obtained from considering Satan, paperclips, and whales simultaneously. It is only of interest when all three things are relevant to making a decision.

Ok good, that's what I was intending to do, maybe it should be a bit clearer?

Incidentally, there's a typo in your quote about Re: 103 should be 10^3.

Shamelessly ripped from wikipedia; their typo. 10^3 does seem more reasonable. Thanks.