Force Carb 3 Gallons in 5 Gallon Keg

I brewed a 3 gallon batch and want to force carb it in a 5 gallon keg. Should I just do it the usual way*, or do I need to take the extra headspace into account? I want to enter this beer into a competition in about 3 weeks. After it's carbed in the keg, I'll use the Beergun to transfer it to bottles for submission.

Thanks.

*usual way = set the regulator to the desired pressure (12psi @40 degrees in this case) and wait a few weeks.

 

Only difference is that it will take slightly less time to reach full carbonation level.

 

I would also purge the air out of the head space as best you can. a few low pressure burps with a little time between each should take care of it.