It did work!
For those who find this thread in the future, achieving this is as easy as going to the "Installer Settings" tab on the app builder, clicking the "Advanced" button, and unchecking "LabView Run time Engine". When the program is installed, it will use the RT Engine already on the machine, so don't mix application builds with different LabView revisions if you do this!
Thanks Chris_C! You've saved me hours of time!