I recently had the starter cable on my '68 Road Runner burn up and short on the headers. I did my best to route the new cable in such a way that it won't touch the headers, but there are still a couple of places near the starter where the cable is only about 1/4" away from the header tube (and the engine shakes quite a bit when running). I also used a heat sheath to cover the cable, but I don't have too much faith that it'll help long-term. Should I try something like header wrap to help insulate the exhaust near the cable? Any other suggestions?
Thanks in advance for any help.

Do you have a pick-a-part salvage yard near you? Many late model vehicles have excellent heat shields and insulation on everything from A/C lines to fluid lines. All styles and sizes. I have boxes of them that I keep to choose from when myself or one of my buddies run into this problem. I like to use the insulated tubes for starter wires. The stuff is dirt cheap, too. Just a little time and effort to find and pull 'em.

That heat sleeve in the link is probably not adequate.
Use "fire sleeve", which is insulated tubing with a silicone cover - typically silver or reddish color.
I've run it next to headers on race cars and it has held up.

Thanks for the suggestions!

Get a longer cable and feed it from the top above the starter to get it away from the headers

Yep.