Thirded!!
But that doesn't inhibit the inner geek in me from wanting to he'p fix up those unfortunate 2nd genners.
Here's what I'm, thinking:
Why not just solder the new beefy ground wire(s) to the outer faces of the spiders. As I mentioned before, you can do that with higher temp solder, which will make it less likely to melt if the connector were to get hot for some reason in the future. But, this may be a moot point, since the whole point of the added ground wire it to reduce the heat in the connection, and the melting temp of regular solder is much higher than the white plastic connector bodies anyway. You won't have changed any of the rest of the harness, so the original ground will still be in place.
Since you'd be soldering the additional ground wires onto the spiders on a workbench, there should be no worries about overheating the harness or connectors while soldering (big honkin' soldering irons apply) and you can slobber the connection with plenty of flux for a good connection, then clean it all up before use.
Wire mechanical support could just be a tie wrap to the rest of the wire bundle a little below the spider with a small amount of slack between for strain relief.