Found the solution. This explanation may not be 100% accurate.
Bundle remembers how it was first executed in the directory '.bundle'. Subsequent executions use this information. 'bundle install' puts the gems in the vendor/bundle directory. 'bundle package' puts the gems in the vendor/cache directory.
Apparently in the first engine I ran 'bundle package' first and in the second I ran 'bundle install' first. To fix the problem, I deleted the vendor/bundle, vendor/cache, and .bundle directories and then ran 'bundle package', recreating the vendor/cache directory but not the vendor/bundle directory.