Joel,
Yes Pro/MECHANICA could probably solve this problem. However, if your picture is right and the assembly has as much clearance as you show in the pictures it may be a little tricky.
The contact region tells mechanica what surfaces may come in contact during the analysis. That said this contact surfaces do not carry any tangential load (i.e. friction) only normal load (contact force). If the two surfaces start to slip between each other during the analysis(no Friction) then the analysis will fail. The work around will be to try to start the analysis in the position at which the surfaces are in contact or close to be in contact. Also sharp edges will crate singularities, therefore, a small round should be applied to the edge and the surface created from the round should be specified as s contact region. I hope this information helps
Luis