I might be visualizing this wrong, but I'm thinking of a (planar) parallelogram linkage setup where the assembly bears upon itself at full extension (the moving stop?). How are you modeling the pin-joints of the 4-bar linkage?
If this were another FEA program, 5 hours would sound like the assembly is unstable and the software is fighting rigid-body motions.
If you're ok with assuming there is no slip/sliding between the stops you can simplify the analysis by 'bonding' the two surfaces of the 'stop' together. Caveats to this approach depend on the flexibility of the remaining structure. Simply bonding the structure may create a false result if it allows for transfer of a moment between the two pieces (like a weld). But if it's simply a normal force you should be good. Stress at the bond will be incorrect but elsewhere it can be reasonable. Computationally a 'bond' is easier than a contact surface. In that 'other program', quadratic Tets are notoriously computationally expensive when used in contact.
Alternatively you could try using a 'PIN' between the stop surfaces if they have concentric features. Again, stress around the 'pinned' surface will be invalid but you can extract the pin loads and do a hand calc.