Ok at the top of the brake pedal it rides on a bushing with a shaft that goes through it and i bet yours is binding or locking up on it. Look at the top around #1 and this is the area i am talking about. you could try to lube but it would be safer to install new bushings or replace brake pedal assembly. Please remember to hit the green accept button.
Does the F350 have a vacuum booster or hydro boost running off the power steering pump?
Sorry about that. I looked over the symptom chart in the shop manual. Make sure that the check valve was replaced when you replaced the brake booster and make sure you have good vacuum to the booster.
Here is the symptom chart I was looking at.