FWIW - The thermal breaker trip point is determined by average current.
Hence, anything that increases the current draw can trip the breaker.
Already know that changing to a segmented carbide cutter head increased current draw.
Here is a list of other things that can increase the current:
Line voltage deviation - If a 120v nominal line is actually 110v in the shop; the current is 8% higher.
Feed wire length - If the length of supply feed wire; including wire from panel breaker to wall; plus the extension cord is more than ~120ft: there will be an unwanted voltage drop due wire resistance. Typically if 120v circuit wire length is over ~150ft for a heavy loaded induction motor, have to increase wire size.
Feed wire sizing - The resistance and voltage drop on normal 14AWG nomex wire used for 15A residential circuit is higher, than 12AWG nomex for 20A circuit (with same load). If you have individual wires in conduit; 14AWG THHN is sometimes allowed for 20A circuits, due it's higher allowed temperature rise .vs. nomex; but it has limitations when used with motors.
Suggest you hook up an ammeter and voltmeter to measure current draw during operation. This will show you why the thermal breaker is tripping.
Once you have DATA; there might be a way to reduce the nuisance tripping.
For example:
If your local line voltage is ALWAYS low (105-110v); then increasing the breaker value by 5-8% could be a solution, as long as you are not exceeding the current draw on feed circuit.
If the line voltage is only low during milling; then might have a feed wire length/resistance issue; which means a larger AWG extension cord and/or larger AWG wire to outlet could help reduce voltage loss.
BTW - Any of these changes should only be done by a trained professional.
Proceed at your own risk.
Be safe, not sorry.