If you look at an example on how to perform spektrum-to-spektrum analys it might be helpful.
Basically, say that you apply you load in dof T1, you should be able to combine that with constants in T2, T3, R1, R2 and R3. This will give you a singular solution for a static load due to one rigid body motion. But sol 111 should work as far as I know. Provided I understand you correct.
I would not "play" with the bailout card for other reasons than "error detection", the limitation are there for a reason.
Good Luck
Thomas