Hey Emanuele,
Looking at the template which drives the event meta within the dashboard, it does appear that there would be a straightforward way to move those elements without overwriting the plugin file. There are hooks in there to add additional fields anywhere you would like though.
An alternative may be to look at the Community Events plugin and have the client enter events via the front-end form there. Those front-end templates can be easily overwritten within your theme following our Themer’s Guide to be any order that you would like.
Thanks!