I’m not sure how you got a 16mm cutter into a 12mm collet unless the shank was reduced which is guaranteed to add flexibility just when stiffness is required. With MT2 spindles being like wet noodles the Clarkson Autolock arbor that came with our Tom Senior that originally had a MT2 spindle was equipped with a knurled fine left hand threaded nut that was tightened against the end of the spindle to greatly increase the stiffness. We have a set of R8 direct fitting collets which only get used when minimum Z height clearance is a problem with large jobs, they certainly add stiffness and can hold up to 20mm shanks.