Avoiding RF noise from MR scanner
What you're trying to deal with right now is generally called "electromagnetic immunity" of a device. Your device has to operate is a very harsh RF environment and still maintain a level of performance that it showed when operated in lab conditions. A typical quick-fix attempt would be to add ferrite beads to your cables just outside and/or just inside the shielded box. Consider them for power and signal cables alike (minus the optical fiber).

However, given the very strong field produced by the MRI, additional interference mitigation may be necessary. Be sure that each chip has sufficient power supply bypass capacitance to avoid conducting RF from the supply to the chip's I/O. Your thought of using low-pass filters on the signals is a good idea, but remember that the filtering will reduce the signal slew rate and add propagation delays. There are ferrite chip inductors specifically intended for suppressing high-frequency noise. You can even find common-mode choke chip inductors that would work for your outputs. Since your outputs are current sources, the additional DC resistance shouldn't be a big problem.

You haven't indicated what construction method your device uses. My advice is geared towards PCB designs. The stray wiring of some styles of prototyping could make managing electromagnetic immunity much more difficult.