As an alternative to pre-building the vignette, have you considered the option --ignore-vignettes? This will avoid prevent R CMD check from throwing any WARNINGS even though the built vignette is missing.
To test this, I forked your repo and updated .travis.yml to use --ignore-vignettes instead of your before_script step to copy the vignettes to inst/doc/. The Travis builds passed without any WARNING.
I'll end up deleting my fork, so for any potential future readers, checking the package while ignoring the vignettes can be done with the following steps:
R CMD build --no-build-vignettes --no-manual .
R CMD check --no-manual --ignore-vignettes --as-cran *. tar.gz