Even after boiling water contains something like 2-3 ppm DO at 1atm.
I thought that boiling gets you < 0.5 ppm and that the uptake was then around 2-3 ppm per hour at 1 atm.
The accepted limits for DO in finished beer are ideally below 20 ppb, should be at least below 50 ppb, and more than 100 ppb patently unacceptable.
Those are some pretty high standards! Especially for a gallon of home brew.
Even when diluted 1/3 gallon water mixed into a total 1 gal gives you a reasonable 1ppm DO, 10x the accetable upper limit and 50x a target level.
We are not taking about finished beer here.
NOW these figures don't factor in that yeast will scavenge oxygen pretty quickly (hence why bottle conditioned beers are, all things equal, more resistant to oxidation than non-bottle conditioned), but as preliminary oxidative reactions occur likely even faster I still would do whatever necessary to minimize the water volume. (If you measure DO at transfer out of fermenter and then again the next day it goes down not because it's improving but because the oxidative reactions have already happened).
The figures are pointless without factoring in the yeast scavenging.
Going forward, the best way to fix gravity problems is blending.
Commercial breweries that dilute beer with water use water deaerators to strip all the oxygen out of the water first (far beyond what boiling can do)