05 Peterbilt 387 Shifter cover bolts rusted and stuck.

Mine broke on the boot trim, the cover plate and the siill plates. The shifter cover plate on my 386 just has clips that are easy enough to change.
McMaster-Carr

I ground down the top flange on the sill nuts and punched them through. Drilled it out to 9/16" and used:
McMaster-Carr

 

Hit the heads with a hammer several times to shock it and break up the rust.

 

May have to just bite the bullet, drill the nutserts out and put new ones in.

 

Impact screw driver or small bolt extractors does trick for me. The screws are 1/4-20, so I usually replace with stainless hex head bolts.

 

If need be..
Harbor freight to the rescue.

 

Clean the heads out good first. Alot of the issue is with all the dirt stuck in them not letting the screwdriver bite. I chuck up a #3 phillips in my cordless impact with all my weight behind it. Either pulls em out or breaks off the head. Once the cover is removed, the clips can be cut with a cutting wheel and fall out easily. Rear 2 ones will be nutserts and suck the most. I think 387s are all clips though..

 

Possibly. S62-6012 is the part number for the repair kit. The other document shows how to assemble it.