Pro/Mechanica's beam elements do have 6 DOF's. This is due to the shape functions that are used to model both translations and rotations that occur throughout the length of the beam.
Solid elements in mechanica only have 3 DOFs (translation only). Rotations throughout the domain of the solid element are not modeled within ProMechanica. Tranlations are the only displacements that are modeled throughout the domain of the element via interpolation using the polynomial elemental shape functions (i.e. order of 1 thru 9).
True the solid element in mechanica and the beam element have two different formulations throughout the domain of the elements themselves, however the element connectivity is handled at the common node. A beam element cannot be connect to a solid mid way along the lenght of the beam element. If it appears that this is occurring in your mechanica model it is because a new node has been added along the length of the beam, thus dividing the original beam element into two new beam elements. Given that the displacements are calculated at the nodes, the difference in elemental shape functions is irrelevant. The beam and solid elements will form their couple at the connecting nodes.
However, the connection between shells and solids in mechanica is totaly different. At the interface between a shell and a solid element, a link element is created. This link element ties the edge of the shell element (which has 6 dof's 3 trans and 3 rot) to the side face of the solid element. In this case the link element is required to couple the displacement of the two different elements at along the entire length of their respective interface. Link elements show up in mechanica as dotted pink lines.
The "waggon wheel" method is classic method that works fine. One alternative is to model the head of the fastener as a shell with a diameter (or shape) of the fastner head, then connect the center of the shells using beam elements. This, in essence, is what mechanica is doing in its "fastener feature". Also, as mentioned above, simple beams from the center of one hole to another with rigid links between the ends of the beams and the edge of their respective hole works great too.
Any of these idealizations is going to produce a stress field result that will not represent the real world conditions, because...they are idealizations. In addition, some could create singularities. However, if the stress, strain, displacment values of interest are far enough away such that they are not affected by any singularity then the results from any of the above methods should be similar.
Good luck.
Steve