"big resistor" seems wirewound: 3k5 WW 5% 5W 20ppm on the 87, 867, 27 etc. in series with PTC.
I think I see 1k ohm probably MOX (green body) on Asian DMM's, Brymen.
Carbon comp power-resistors are expensive and end-of-life now, drift is terrible.
Porcelain-coated nichrome is pretty good for surge power handling, but turn-turn voltage breakdown might be the limiting factor.
I never did find much short-term (<10msec) impulse data/overload specs for resistors. Did an automotive load-dump design running a resistor at >100X overload and worked with
Vishay engineers on it. It was hell because the SMT WW resistor's thermal properties, wire melting point were modeled.
A 6kV impulse, couple 1.5kV (clamping) MOV's, 1.5kohm PTC and 3.5kohm 'big resistor", that's only 0.6A instantaneous or 1.3kW for it, and 0.54kW for the PTC. Hmmm.
If my numbers are reasonable, 250X overload but really brief but really big...