I have a 5 gallon batch of beer that I want to split between kegging and bottling. I have a 3 gallon corny keg for this. Per a forum member recommendation, I currently carbonate my 5 gallon cornies by applying 30 psi and shaking vigorously for around 5 minutes. Then I let it sit on that pressure for 24 hours. This method works great by the way.

Do I need to adjust my procedure (psi setting, time of force carbing, etc.) for a smaller volume of brew in my 3 gallon corny? If so, what are your recommendations?

Do it the same way with the 3 gallon. The results will be the same. Or you could just let it sit on 28 psi for 48 hours, bleed the 02 off and set the psi to what you like to pour from. Comes out perfect for me every time.