With two beams per foot on the outside edge of the foot, Mode 1 is now 34 Hz and Mode 2 is now 41 Hz, and Mode 3 is 61 Hz, which is the engine rotating about the Z axis through its center of mass.
There is still bonded contact to the engine at the top of each foot.
I switched to the Direct solver, and the solution was computed in 4 minutes on 9 cores with 94 GB of RAM allocated.
My comment about static structural was that you could calculate the stiffness of the foot in order to compute the natural frequency without running a modal analysis. Prestressed modal is probably not important but is simple to do it and see the effect on the result.