As far as I know, there isn't one (that isn't PC-Lint), which is a shame, and surprising. I've seen the suggestion to do this bit of pseudocode (which is basically automating your "painstaking process":
for every cpp file
for every header include
comment out the include
compile the cpp file
if( compile_errors )
un-comment out the header
else
remove header include from cpp
Put that in a nightly cron, and it should do the job, keeping the projcet in question free of unused headers (you can always run it manually, obviously, but it'll take a long time to execute). Only problem is when not including a header doesn't generate an error, but still produces code.