2004 F150 4x4 rear end shudders so what do you recommend for a better than stock limited slip to replace it?

 

If it's worn or damaged gears, then I would replace the entire rear end with a used one that's known to be good. Just remove your old one and bolt in the replacement. Often you can find them online or at a junkyard for just a couple hundred dollars.

If you're wanting to just install a limited slip of some sort, I would go with an eaton truetrac.