TL;DR
Finally came up with a clever way to do this with minimal changes to the lecture material. Check it out!
If this looks good then I can add the rest of the lectures and be done.
What I Did
Each Julia Markdown Document gets weave-d with a custom md2html template, and the generated output is used to build the page along with all other layout components (such as head, nav bar, and foot) through the Franklin.jl build process.
This seems to be the best route because it allows the lecture notes to remain untouched (except a couple additions to the front-matter). I considered using Books.jl, but this requires fairly significant changes to every code block. Converting every *.jmd to a Literate.jl script would take less time and use the builtin Franklin.jl support, but I decided not to spend time converting everything. These other routes are of course options, but I think this choice achieves a happy medium of clean site and minimal work. Any desired changes should be possible with some CSS tweaks.