I.. I liked my suggestion. Reputation would be cool :/ Also, changing init settings feels too easy for me, and (counter to that) I hate that I have to save, exit, change init, and then load again each time I decide my immigration policy needs revising.
Plus, the option-richness is awesome, and would add a lot more depth to immigration.
On physically preventing immigration: Border patrols should be a thing, perhaps via a squad designated from the noble, just like a captain of the guard or hammerer. This squad would then have a schedule order available to literally patrol the border, with their patrol route being preset (i.e. the edge of the map) by the game. Depending on the amount of time per year they spend patrolling (i.e. doing the preset schedule order), the amount of dwarves in the squad, and so on, you get a bonus to any negative modifiers you applied for immigration - i.e. less chance of unwanted dwarves immigrating, plus faster reputation gain.
Come to think of it, you could simply make it an option available to any squad in the scheduling screen: train, protect burrows, patrol, or patrol border.
Then, as above, you'd get bonuses to negative modifiers based on amount of dwarf-hours spent patrolling (two dwarfs patrol for 2 hours = 2 dwarf hours patrolling) per migration wave.
When migrants arrive, your immigration officer has meetings with each migrant, the desired ones become part of your fort, and for the undesired ones who came through despite all your patrols, a screen pops up set out like the units lists where you can choose which of the undesirables to turn away.
The undesirables turned away would have a chance of either becoming berserk, or leaving peacefully, with an option to give them food as a way to influence the chances of peaceful leaving.
Having family members or friends turned away would be a very big negative thought for dwarves in the migrant wave or in the fortress.
I believe that that would allow realistic immigration control for players, which isn't in any way too easy or anything, nor too hard. It also gives greater incentive to not turtle, since without access to the map edges, you can't prevent the influx of migrants who need to be memorialised.