[franken]

There's more current than should be going through the things hat are getting hot. Its that simple.

Adding grounds, while possibly needed will allow for more current to flow, and you may find the fusible link then cooks.
I'd measure from the closest ground to the positive side of the fan, then direct from the battery ground to the fan + side. Poat the results.
I wouldn't run a fusible link through that ribbed tube since its going to melt if the link gets hot.
I see in the OP's pics that there are several connections to the + battery post, as well as a single post junction block. Nasty. I'd get a junction block w/ multiple possible connections from a square--they're mounted to the FW above the passenger side valve cover. Maybe mount it on the passenger a bit behind the normal location of the original JB. I'd also probably mount the relay for the fan (or maybe all of them) near the junction block on the fender.

Then start asking when is the fan running?