Solvents adequate for dissolving overheated polyethylene terephthalate glycol-modified (PETG) residue?
It is difficult to tell when you consider PETG overheated (how long? what temperature?). Thermal degradation likely produces several reaction products each of which having different solubility in different solvents. So I don't know whether I ever encountered "overheated" PETG during my own 3D printing experiments.

But I have had very good experience with Tetrahydrofuran (THF), which I happened to have in my basement for a long time (beware of peroxides!) and I have finally found an application for. It dissolves freshly printed PETG (and glue parts together) as well as the residues on the print nozzle.

Side notes: Acetone is wellknown for being absolutely useless for dissolving PETG and I can confirm this from my own experience. All you can expect is to roughen the surface a little bit.

You can read several reports that say dichloromethane is not working as a solvent for PETG. I have found a report that claims Cyclohexanone is working. But I haven't got personal experience with these both. Toluene neither.

But in general, the best method for cleaning nozzles is brute force, i.e. pyrolysis by bringing the (brass) nozzle to red heat with a gas torch. Fast (takes only a few minutes) and reliable (absolutely no residues, expecially at the nozzle hole). One thing I have noticed is that it is a good idea to polish the nozzle with finest steel wool after pyrolysis, especially the inside. On the inside this polish reduces friction for the filament (the brass gets "hazy" after heating it with the gas torch). On the outside, having a shiny surface may reduce emissivity/absorbtivity a little bit, which helps keeping set temperature during printing.