This photo shows the window setup. From interior to exterior: sill, interior vinyl ridge, vinyl recess, exterior vinyl ridge, vinyl decorative trim (non-weight bearing).
This photo shows a closeup of the vinyl ridges on the sill area. These ridges likely would not support the weight of the air conditioner without damage to the window. Hence, we needed to build a platform to shoulder the weight of the air conditioner instead of the vinyl ridges.
This photo shows the platform we built to support the weight of the air conditioner, instead of the vinyl ridges. The platform consists of: a 2" x 4" on the window sill, a 1" x 2" in the vinyl recess area between the ridges, and a piece of plywood to bridge the two.
This photo shows the upper support we built to hold the air conditioner securely in the window. It consists of two 1" x 4" pieces slightly offset from each other vertically. The offset enables the retaining "lip" attached to the top of the air conditioner to fit beneath the lower 1" x 4" more snugly, and to get a retaining screw more securely in the wood.
This photo shows the finished project. Note that the 1" x 4" facing the interior actually slides into the groove of the retaining piece on top of the AC unit, which should provide a more secure hold. The bottom sits up on the platform because we need to rip the platform bridge into two pieces, enabling the bottom "lip" on the AC unit to sink into the platform so that the unit sits more flush. Until we make this change, we have filled the small space below the according folds with insulating foam to keep air and bugs out.
The air conditioner has functioned smoothly since installation. There is no vibration or obvious stress to the window frame (yet!). We have cold, snowy winters, so this approach is nice in that it can be disassembled within minutes at the end of summer, and then easily reassembled and installed the following year. Cheaper than central AC!
Thanks to Jason Kasper's helpful "Double Hung Vinyl Windows and Air Conditioners" page for the inspiration on this project.