I have no experience with Kirby, but here's how to get Dropbox working on Openshift.
The following is a combination of doing a Dropbox install on a server and doing it in a non-standard location. Everything gets done in $OPENSHIFT_DATA_DIR because that's where you have write privileges.
First, make sure you're in $OPENSHIFT_DATA_DIR
cd $OPENSHIFT_DATA_DIR
Next, download the appropriate version of Dropbox:
wget -O - "https://www.dropbox.com/download?plat=lnx.x86" | tar xzf -
This should give you the .dropbox-dist folder in $OPENSHIFT_DATA_DIR.
Next, tell Dropbox to start the installation process, but tell it that your home directory is actually the $OPENSHIFT_DATA_DIR:
HOME=$OPENSHIFT_DATA_DIR ./.dropbox-dist/dropboxd start -i
Follow the instructions to link your Dropbox account to the Openshift server. After it's linked, it should start syncing everything in your Dropbox account to $OPENSHIFT_DATA_DIR/Dropbox. This might be a bad thing for you because you have too much data in your Dropbox account. If so, then you should exclude folders.
You can do that with the CLI script that Dropbox provides. Still in $OPENSHIFT_DATA_DIR, download it:
wget -O dropbox.py "https://www.dropbox.com/download?dl=packages/dropbox.py"
Make sure it's executable:
chmod +x dropbox.py
You need to run it the same way you would Dropbox:
HOME=$OPENSHIFT_DATA_DIR $OPENSHIFT_DATA_DIR/dropbox.py -h
Hope that helps.