I have now tested exporting the same AppleScript from Script Editor 2.11 (203) on 10.14 beta 10 (18A384a) and this appears to produce an application bundle that will prompt for user permissions when run on the same Mojave beta.
I can see that the exported app bundle's info.plist includes these keys which do not appear in versions exported from previous Mojave betas (<= 7):
<key>NSAppleEventsUsageDescription</key>
<string>This script needs to control other applications to run.</string>
<key>NSAppleMusicUsageDescription</key>
<string>This script needs access to your music to run.</string>
<key>NSCalendarsUsageDescription</key>
<string>This script needs access to your calendars to run.</string>
<key>NSCameraUsageDescription</key>
<string>This script needs access to your camera to run.</string>
<key>NSContactsUsageDescription</key>
<string>This script needs access to your contacts to run.</string>
<key>NSHomeKitUsageDescription</key>
<string>This script needs access to your HomeKit Home to run.</string>
<key>NSMicrophoneUsageDescription</key>
<string>This script needs access to your microphone to run.</string>
<key>NSPhotoLibraryUsageDescription</key>
<string>This script needs access to your photos to run.</string>
<key>NSRemindersUsageDescription</key>
<string>This script needs access to your reminders to run.</string>
<key>NSSiriUsageDescription</key>
<string>This script needs access to Siri to run.</string>
<key>NSSystemAdministrationUsageDescription</key>
<string>This script needs access to administer this system to run.</string>
I wonder if these keys can be manually edited/reduced to just the capabilities that will match the expected functionality requirements of the script/app bundle?
The recent beta 10 (& possibly the untested 8 & 9) looks like it has resolved the main issues with no permissions prompt that would allow the user to let the script proceeed.