... I'm measuring 154.1 and 154.4 volts AC going to Diodes D301 and D302 from the power transformer. I believe it should be 128 volts AC as read on the schematic.
Please check this because this could be the reason why R316 has to drop so much voltage.
How are TP301 (+150V), TP302 (+130V), TP303 (+40V), TP304 (-30V) ?
It would tell if the power transformer is hyper, or the loads on 150V, 130V are too light and causing the raw DC voltage to be high.
It's a badly distorted sine-wave at the transformer secondary, so your multimeter may not read true RMS.
My poking around in LT Spice I'm still getting high ~5W power dissipation in R316. I don't have all the flyback transformer's data (winding resistances, secondary inductance etc) but made some estimates.
170V raw I get Peak 225mA, Average 50mA, RMS 100mA current through R316 for 4.7W and a 3W part would be past the limit over 200°C.
Careful a thermocouple does not connect to the resistor if paint or ceramic is chipped, you would get a hazardous live thermocouple which is dangerous. A spot IR temperature reading might be enough.
Before going into any notion of changing the factory design, best we agree if things are normal or not for R316.