I had some oscillation problem with the max1771,
the shielded box helped a lot, shielded wire too, but the supply layout is also very important.
Try using a small capacitor between feedback and ground, and between HV and ground, something like 100~200pF, that should remove the high frequency oscillation.
Before the amp B+ add a low value resistor in series and another capacitor, that will form a low pass filter.
Look at the layout, the signal should be far from the inductor, and if possible use a ground plane under the inductor. Depending on the type of inductor you will have more noise (radial) or more voltage drop and heat (toroidal), I don't know if my inductors are the bad type or what, but I experienced this issues.