How to make a modified dmg distributable?
You cannot modify the DMG and have it still pass trough GateKeeper without re-signing it. This is basically the entire reason for having the code signature!

Basically you have three options:

1) Remove the old code signature and re-sign the DMG with your own signature. This requires you to be enrolled in Apple's Developer Program.

2) Distribute the original, unmodified DMG - and accompany it with your own modifications. This could be done as instructions for the user on what to copy over, or it could be in the form of an automatic script.

3) Remove the signatures completely (both from the DMG and the app). The user then needs to have GateKeeper set to allow opening unsigned applications (i.e. the user will be prompted on the first open).