Thanks for the replies!
Whilst I was aware that gate capacitance could be a problem for the op-amp, I simply searched the LTSpice list for 'fairly low gate charge in comparison with the others in the list'. I should have checked more carefully, especially in relation to the chosen op-amp's output charcteristics.
Good point about the size of signal excursion required to drive a 'gate' in comparison with a 'base'.
I've used MOSFETs successfully in the past for about 20mA, for example BSS138+MCP6005 or TN0200K+TLV2624. This perhaps made me too confident.
I'd like to be able to model this such that I see where & how the problems arise. Maybe an ideal op amp plus some parts to model the LT1797 output characteristics, then some capacitance(s) to model the gate charge. Then use an ideal buffer to drive the BJT, and see what it takes to spoil the BJT's good performance.
I am especially curious about the way the MOSFET used in the simulation seems fine at lower currents - this might tie in to the point about size of signal excursion?
A complicating factor is that gate capacitance varies with gate drive - the capacitances are voltage dependent I seem to recall.