first of all - you cannot express right-handed matrices with Cinema's
Matrix type, because it is explicitly left-handed. It has been discussed in a scenario similar to yours here.
But you can of course simply compute a frame reflected on one of standard basis planes, which will give you the right handed frame for a given left-handed Cinema
Matrix (or vice versa). This topic has been discussed just recently in great depth here.
Your question is also a bit ambiguous. You state twice that you want the frame to be expressed as a position, direction and up-vectors (plural). The position would just be
Matrix.off, and the direction and "up vectors" would be just the axis components of the Matrix, i.e. the attributes
v1, v2, v3 of a
Matrix. What is what is depends on the systems you want to convert to and you will have to consult their documentation on how to interpret the rather ambiguous up vectors.