I know of folks who have overcome low prestige D2 Sim AI's to get a recruit at D3. I've never tried it myself, so can't offer any strategy insights other than I'd probably wait for the first FSS Word on the Street to see how tight the recruit is to the Sim so as to not throw limited resources at a player who's very tight or such.
As for how prestige works, my understanding is an F prestige for the higher division comes in after an A+ at the lower division, so you're not quite two full letter grades prestige-wise behind the D2 Sim. Keep in mind that the mileage does not apply to the Sim (all Sims recruit as if they're 200 or 250 miles from the player...I can never remember which figure is right), so the fact it is 580 miles is irrelevant -- it's recruiting as if it is closer to the target player than you are.
Good luck if you try for it!