You might try blocking off that part of the map edge. Build floors over any up ramps on the map edge (you can't remove them with mining designations, but constructed floors will get rid of them), then build drawbridges, link them to a lever, and raise said bridges to make a pseudo-wall right on the map edge; this will prevent anything from spawning where a raised drawbridge sits.
The other option is to have a tunnel that opens to near where the migrants spawn. Trap it thoroughly so few enemies can get in there, set burrows so that your prior residents aren't allowed into it, set a meeting area inside, and make an airlock around the meeting area. Some migrants, at least, will go to the meeting area inside the tunnel, so they'll have less distance to run in the open, and once all the migrants are inside or dead you can switch the airlock, put the new migrants into your main fort burrow, and have them go to work. Due to the airlock, few enemies will even try to go in there unless you've got migrants, so little looting will occur inside either.
Finally, to get more migrants, make lots of created wealth and have little imported wealth. Sew images or sell any goblin clothing that shows up, melt foreign-created metal equipment, decorate any foreign bins or barrels you get, and make high-value stuff like steel and silver serrated discs, aluminum and platinum furniture, and the like. Created wealth attracts migrants, while imported wealth seems to repel them, so turning imported wealth into created wealth is a good plan.