I’m having a shudder noise/vibration at slow speed take off while turning

I have the 9.75 rear end with the open clutch style differential. I’m having a shudder noise/vibration at slow speed take off while turning. Looking at several ways/options to go about this solution. Trying to rule this out but I haven’t messed with the brakes yet on the vehicle since I owned it. But the parking brake light stays on. I know the rear and front pads need to be changed but haven’t looked at close enough to see if any of the rear disc brake components are defective and seeing if this could cause the issue. If it is the rear end solely I would like to know what you think about these 3 solutions and if a better one (if the brakes do not fix):
1. Change rear differential fluid and add friction modifier. Cheapest but do this just to see if this fixes?
2. Replace clutches and re-seal, new bearings if damaged? Probably the next cheapest solution but seems complex and labor intensive getting clutches and components lined up and assuming the ring and pinion gear along with any other rear end components are good to go another x amount of miles.
3. Replace differential with an Eaton Truetrac. While at it probably replace ring and pinion, all bearings/seals? Most expensive by far. And would it be worth replacing ring and pinion if going this route?