I don't know of smaller Ubuntu MATE-specific image, but you can uninstall nearly everything. The first thing I typically do after installing (before downloading updates!) is something like
sudo apt remove hexchat libreoffice* thunderbird shotwell
Just watch for anything unintentional before you accept the uninstall. I think some core apps can't be removed, but it's a small list. (With 16.04 and before, the meta-package
ubuntu-mate-desktop will get removed if you remove built-in apps, which is not a real problem, but it's been resolved in 16.10 and newer.)
As you say, the Activities Overview is really more of a GNOME 3 feature than a Fedora-specific feature. If you really want that, you probably want Ubuntu GNOME! I don't know of anything for MATE that matches it completely, since it's an combination of a launcher, an app dock/menu and window overview. There are menus, like the in-development Brisk Menu and launchers, like Synapse and Albert (which I use), which you may be able to bind to the super key.