Ray,
Consider the following game plan:
Start out with a commercial 12 x 12 or 18 x 18 patio block. This will provide both a good flat surface to build the crossing on, but also a stable surface under the crossing after installation.
On the patio block, anchor bolt four independant brass plates (sheets) under where the frogs are going to be, but NOT touching one another.
Build the crossing in one congruous piece soldered to the four brass plates. (remember the four brass plates are anchor bolted to the patio block - preferably two bolts per plate to promote stability).
After the crossing is completed, make the desired cuts to isolate each frog. In lieu of putting styrene in the saw cuts, I would recommend a two part epoxy that can be filed smooth on the inside and top of the real head.
No place the completed crossing mounted on the patio block in the desired position on the layout. This will provide the stability you are looking for. It will not provide a prototypical appearance, but will be almost bullet proof.
I have not used this system, but being a mechanical designer, this is the process I would use for your circumstances. Credits to Craig and Bob for their earlier input. I just added my twist.
Bob C.