I managed to solve this by finding all of the required packages on the Linux Packages Search website. It's a bit of a sloppy method, as it involves downloading and installing several DEBs. I don't know have the know-how, time, or patience to set up and maintain a repository, so if you are just as desperate as I was to get this working again, you can use this method.
CLICK HERE TO DOWNLOAD ALL OF THE REQUIRED PACKAGES (TAR.GZ / DROPBOX)
HIERARCHY OF DEPENDENCIES
indicator-messages-gtk2 (=0.6.0)↳ depends indicator-messages (=0.6.0)
↳ depends libindicator-messages-status-provider1 (>=0.4.92)
indicator-session-gtk2 (=0.3.96)↳ depends indicator-session (=0.3.96)
indicator-datetime-gtk2 (=0.3.94)↳ depends indicator-datetime (=0.3.94)↳ depends libecal-1.2-10 (>=3.2.3)↳ depends libedataserver-1.2-15 (=3.2.3)
↳ depends libedataserverui-3.0-1 (>=3.2.3)↳ depends libcamel-1.2-33 (>=3.4)
↳ depends libebook-1.2-13 (>=3.4.4)↳ depends libedataserver-1.2-16 (>=3.4.4)
↳ depends libecal-1.2-11 (>=3.4.4) INSTALLING THE MESSAGES INDICATOR
Install the packages in the following order: libindicator-messages-status-provider1 ⇨ indicator-messages ⇨ indicator-messages-gtk2
INSTALLING THE SESSIONS INDICATOR
Install the packages in the following order: indicator-session ⇨ indicator-session-gtk2
INSTALLING THE DATETIME INDICATOR
Install the packages in the following order: libedataserver-1.2-16 ⇨ libebook-1.2-13
⇨ libecal-1.2-11 ⇨ libcamel-1.2-33 ⇨ libedataserverui-3.0-1 ⇨ libedataserver-1.2-15
⇨ libecal-1.2-10 ⇨ indicator-datetime ⇨ indicator-datetime-gtk2.
Once all the required packages are installed, kill mate-panel. When it restarts, all of the indicators should be visible.
EDIT: Don't forget to lock the versions for indicator-session, indicator-datetime, and indicator-messages.
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