Oscillations in Precision Voltage to Current Converter Design
To meet the criteria for an oscillator, you need to have positive feedback at a gain of one or greater.  Your op amp as configured will act as an integrator at higher frequencies, so you have a 90-degree phase shift (in addition to the 180 degrees of the negative feedback) and with the instrument amp's higher gain at the high end, you have met the criterion for oscillation.  The original TI circuit relies on the roll-off of the response of the instrumentation amp (providing lower gain at higher frequency) to stay away from this condition.  If you went back to the original instrumentation amp with its R2C2 roll-off network, your circuit would likely be stable but with the lower, 1 Khz frequency response.

You may also want to consider that, because I = c dv/dt, your 50 uA into a 10 uF load will only provide an output voltage slew rate of 5 volts per second.  At 1 Mhz or even 100 Khz, any change in current will be primarily charging the large capacitor at this very slow rate, so the voltage response at 1 Mhz will be a few microvolts.