I've had issues with 1) failing shiny apps (my own poor code) and 2) runtime:shiny rmds, in that when i close the browser, rscript.exe appears to still be running - is this the zombie process you mention? If i add:
taskkill /IM "Rscript.exe" /F
to the first linke of appname.bat then this solves the issue as it kills all Rscript instances. However, it assumes you dont have any other Rscript instances occurring for other reasons.