My Zenith 24NC31Z quad coil was toast. It crumbled with heat. It was a fairly critical part because it determined the quadrature subcarier phase and the number of turns and coupling were critical. I had the good fortune and presence of mind to study the crumbled mess and carefully count the number of turns of the primary and secondary and the coupling. As it was resonating at 3.58MHz, there weren't many turns and I simply rewound it on a fresh (stripped) former. The former's previous life was a horizonatal oscilator coil!
Worked a treat.
If yours is really bad, that may be a problem. But A burst coil is pretty basic and many sets used the generic circuit. FYI I see a coil available which you may be able to adapt.
https://www.ebay.com/itm/13302283645...cAAOSwNphcPOHO
The thing is that CTC5 parts may show up. But considering the age, this may be the simpler solution.