Is there a way to run the above listed make command with the same
environment as it is run when the error is produced?
$ bitbake <recipe> -c devshell
This drops you in a new terminal with the same environment that bitbake sets up, and in ../temp/ you'll find run.do_compile and so on, which are the scripts that bitbake runs for each task.
(you need to fix your recipe so that it forces the use of ${BUILD_CC} instead of cc)