You could follow the fractional distillation with fractional crystallization. Make sure your glassware is special glassware if you want to go for semi-conductor grade purity. This will likely increase the alcohol content to 95%, if you want it more dilute. Simply add back similarly purified water. You want the vodka to have some of those flavors of actual vodka? Do what the bottled water companies do and add the minerals and flavor notes back to the purified solution. After all, at this point it’s all about a brand because you are way beyond making any real difference in flavor.
Well, shit, I checked the deli by my house, and, sure enough, 151 proof on the label, although it had a little neck-tag on it (added later) where it says it’s original Warsawian 96% Spirytus (in Polish.) Hmmm…
How accurate is the test of burning a specific amount and measuring how much is left? The difference between 4% remaining and 24.5% remaining ought to be pretty clear, if you’re willing to test it out?
I’m pretty sure the OP is interested in “Absolut ethanol” 
Or I could just use the spirit hydrometer I happen to have in the basement and put it to use for the first time (accidentally picked up the wrong hydrometer, once, for beer making.) Now I just have to find a reason to buy such high octane stuff. I have been meaning to make some homemade bitters…
Stolichnaya has a little sugar in it, so it tastes a little smoother, other vodkas also use various tricks to make you think you are not drinking a mixture of ethanol and water when you actually are.
Surely satisfying our curiosity AND making bitters are more than enough reasons to do a thing! 
C’mon, you can tell the SO that the Dopers made you do it! Better than pan frying your semen, right?