I compete quite a bit with bottled beer from the keg. It can be done, but you will lose some level of carbonation in the process. I generally over carb the beer prior to bottling. I run a few "test" bottles to get the dispensing pressure right. You want some foam as you bottle to create a oxygen barrier, so playing with the dispensing pressure will get either no foam or way too much. I try to get about an inch or so of foam in the bottle and allow the bottle to get a little over filled, about a 1/2" from the top. As you "cap on foam" it will burst the top of the foam leaving little oxygen in the bottle. Purging the bottles is helpful to reduce oxygen ingress, but capping on foam is the key. Filling them as full as you can helps as well.
I don't worry too much about the temperature of the bottle, but I try to get the beer as close to freezing as possible. The other suggestion is to wait as long as you can to bottle prior to shipping or entering your beer to get the freshest beer you can to the comp.
At the 2017 AHA convention, New Belgian Brewery did an experiment with a Blichmann gun. They were able to get the oxygen content down to 30ppb just by purging and capping on foam. They were a little inconsistent as far as the oxygen levels in the beer (some were up to 200ppb), but it showed that it could be done.
In 2021 I won 2 silvers at the NHC with a American Lager and an International Lager. Both were filled from the keg a day before shipping. Both beers needed to be pretty "lively" as far as carbonation goes and filling from the keg worked just fine.