I'm sure you are on a better path than what I used, but fwiw:
I used the power fet path for 100mA and 1A stable switched CCS. My requirements were a little different as I was after a transfer CCS reference, or simple bench top reference, which could operate from a 5V USB battery bank, and use an LM336-2.5 that I have on some spare pcbs, and an opamp I had available. The current was stable enough for 6-digit meter transfer, but needed measurement and maintaining a constant burdon voltage, especially for the 1A mode, in order to maintain transfer conditions. I didn't use low tempco resistors, but selected two 10W ceramic block for lowish tempco for the reference R (not as shown in schem below). I used a bypass resistor for the 1A mode to alleviate the FET temp rise.
Regulation from burdon voltage variation was influenced/limited by the FET on-voltage being in the relatively high-gain but non-linear analog region. Thermal stability was influenced by various part tempcos, including FET on-voltage. FET heatsink was live so regulation can be sensitive to external leakage/contact.