2005 Chevy Tahoe fusible link getting hot not breaking thou

Hello, I have a 2005 Tahoe and the remote positive terminal, where the fusible link connects off of to the alternator has begun to melt the Red plastic. The fusible link has not broke, I have recently had trouble with the igntion accessories only coming on when I tilt the Wheel up and down. The vehicle has about 130,000 miles on it and was a former michigan oakland county sheriffs vehicle. I am going to begin by replacing the battery cables and replacing the worn fusible link, suspecting that the harsh winters here in chicago have dirtied up the cable connections. Also I am replacing the brackets that support the positive cable that wraps below the engine to the starter. I bought the vehicle used and the supports for the cable were taken off. My assumption is stress on the cables have made the connections loose/highly resistant over time. I have also recieved a couple of time the "service charging system" message onn the DIC! I have a couple susspected areas where there could possibly be a short or bad ground for the headlights, which I am going to fix if needed beforee replcing links and cables. What could I be missing? Does it sound like I am on the right path.I have been researching al over and cant go ono with out my truck!Hah Ill be awaiting your reply
Thank you for your time