If this was me, I’d would close transfer from the fermenter to the keg just prior to it finishing and let stand at cellar temps.
It will finish in the keg, building head pressure, therefore carbonate naturally, and the yeast will scavenge any oxygen the close transfer process may have allowed in. If you have a spunding valve you can monitor and control head pressure to achieve a certain volume of carbonation.
I’d store at cellar temps until “close final” (aka I need the beer), cold crash, fine w/gelatin thru the gas port if desired, and serve.
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