Sonic02: That is a new one on both of us. It might help to know which JLM opamp you are using and a bit on your test methods?
To expand a bit on Niels comment on the JLM, there is no feedback cap used with a 2520. At least there wasn't one in the original and we haven't used any. There is however a spot for it marked CF, since I didn't know what opamp people would use, and some may want to see one. If you try this, I would try a C0G/NPO or mica cap between 47-100pF.
The resistor in parallel with the cap will allow a bit of DC to get into the transformer winding, and is what API did to "tame" the low end boost in their circuit (I think I may have explained this somewhere, but there is a thread where member Abbey Road d-enfer posted graphs showing what it does). I will look for it and post a link if I find it.
The 1K8 load resistor on the output transformer would change its response, so if the cause of your problems is the JLM opamp's interaction with the outpu trafo, that might help things. If you decide to try this, temporarily putting a 5K trim pot in there would allow you to find the best possible value.
I would first try the CF.