I think you are correct it needs a clutch as I was watching the video the pedal position when the tractor starts to move is almost fully released ,it should be engaging sooner. Does it have a 2 stage clutch and does the pto operate normally? You checked all the pedals roll pins right.
some of these tractors that have a shuttle shifts seem bad about shearing a pins in the levers that change tractor directions but now that I think of it that would not be in your case. But look at all the pedal connections to make sure, I think no two were made the same. What kinda tractor and hp is it anyway?
Unfortunately I don’t have the space to work on it inside and with the temps being 100+ for the next few weeks I didn’t want to tackle this, so I took it to someone to work on. He’s got it but hasn’t split it yet. I’ll update with his findings.