I've figured it out!
I can now access my site at
novulae.tk.
- FileZilla: I'm still doing my FTP through FileZilla, and it's set to use my same old username and password, but now is using "192.241.151.74" as the HOST.
- DOT.TK: I signed up for a free dot.tk domain. Funnily enough, only registering via Facebook actually worked. (I recommend anyone new to dot.tk to only grab a name for ONE MONTH in case the whole thing fudges up that way you can try your desired name again later.)
- FREENOM: Dot.tk does it's stuff through Freenom. Under (Domains > My Domains > Manage Domain) Management Tools > Nameservers, go ahead and use custom nameservers. Mine are NS1.NOVULAE.TK and NS2.NOVULAE.TK, for example.
- FREENOM: I then went under Management Tools > Register Glue Records, and added NS1 and NS2, directing them to the IP "192.241.151.74".
- ZPANEL: Actually visiting 192.241.151.74 gets me the ZPanel, of course. I created a new domain as novulae.tk and used an existing home directory that pointed to my old files under "/novul_99webs_org". (I discovered later that I could rename the folder via FileZilla and delete, then recreate, the domain and point it to a more intuitively named "/novulae_tk" directory).
- ZPANEL: Now I can go into the DNS Manager and edit novulae.tk. All that needs to be done is to press "Create Records" and that's it, the rest is correct.
After doing all that, magically my FileZilla could connect again and visiting the url immediately took me where it was supposed to go. Of course I then needed to hop into my Mysidia's inc/config.php file and change the domain.
So everything's good on my end now, at least. I was really panicking.