Can I restart on the same world somehow? Or will I need to do a new map entirely? I know that I can't just re-embark but I like that map a lot and wouldn't mind restarting.
Did you do a map parameters export any time when worldgen finished or in legends mode? If so there should be a text file someplace in the root DF folder (where Dwarf Fortress.exe is) that has the seed for the world.
I'm not sure of the exact name of the file off the top of my head, I think it would be something along the lines of "Region# world gen param".
If you find it, this is where things get a little complicated.
Open the file and highlight everything from the line starting with "[TITLE:" down to the end of the file, then hit ctrl+v.
Go to data>init and open the file world_gen.txt.
Click at the bottom of the file and hit ctrl+c. It will copy all of the information you had highlighted into that file.
Change the TITLE line of the last entry(the one you just copied into the file) to something unique, but keep it all caps. like [TITLE:MY WORLD] for example.
save the text file.
Run Dwarf Fortress and enter design new world with advanced parameters.
Hit Esc for the disclaimer
On the right side of the screen there will be a scrollable list. Look for an entry with the name you just gave your world. "MY WORLD" in my example and hit enter.
It should now regen your world exactly as it genned the first time. Congrats, you have your world back.
EDIT: Edited for context.