F-250 Brake Issue

I have a 2011 F-250 four wheel drive. A while back I noticed that once in a while there was some resistance after putting it in drive, sort of like a caliper that didn’t want to release. A little push on the gas pedal releases the tension and everything seems fine. Sometimes it does this, other times it does not. I suspected a sticking caliper and had both on the front replaced since it for sure seemed like the issue was coming from the front. I also had both brake lines replaced on the front. Everything was good for about a day and then it did it again. There is not hot brake smell of any kind and it stops straight. My mechanic is stumped as well. The only other thing to do is to replace both back calipers. Anyone else ever experience this issue? It is a 6.2 gasser.