Is hosting your image in an online service (like imgur ?) something you could do ? This way your image would be available to your book as the img tag would linked to http.
Otherwise, you could also build your book using a makefile for example. First executing, render_book then copying the image into the _book folder. Would it work for you ?
An rscript to do that is also a solution.
In fact this is a hidden feature: You can use a Makefile or a _render.R script to be executed to render the book instead of rendering with render_book only. If _render.R is found, it will be executed, if not but a Makefile exists, it will be executed. If none of the 2 files exist then render_book("index.Rmd") is executed.
In one of the two scripts, you can put the logic you want pre-rendering and post-rendering. That is something used by some book like the Rmarkdown book
This is not really documented but you could find how it works by looking at the code of bookdown_site renderer.
At last, I am not sure the discovery of local resource would work for this html line in yml. I'll dig a bit in bookdown code to see about that 