One way to overcome that might be to use ansible to automate:

  1. Dokku setup on a new server 
  
  2. Deploy your app from a git repository

  3. Restore your database from backup

If you aren't comfortable with ansible you can use Fabric [0] or Sup [1]. I think there's even an ansible guide for Dokku deployment on their blog [2].

[0] https://www.fabfile.org/

[1] https://github.com/pressly/sup

[2] https://dokku.github.io/general/automating-dokku-setup