I don't know about BA. but I was able to get answers via email whenever I needed assistance from migraciones (in Cordoba). They always responded within 24 hours (shocking...I know) and I always received a responses. I go that route first in order to have in writing--and articulate clearly in Spanish. Inquiries via phone are harder for me and there's less accountability for them (I don't like talking to five people and getting five+ different answers).
Frankly, I apply this to more than migraciones..I have won many challenges via email and IM chats (yes, IM is great)...In one instance, I cited the law my medical insurance coverage to avoid an illegal USD500 fee that the hospital insisted I had to pay in no uncertain terms whiles I was at the clinic (law printed and in hand at that time AND the insurance has a support desk in the hospital...all worthless)...One day after an IM chat--I received a call from the clinic that it would be gratuita and scheduled the appt. (Sorry, a bit off-topic...point is...anything you can get in writing is great...you've been around the Argie block so this is probably old news)
I suspect this is a bit bigger issue than what can be address via email, but it's good info... It worked well for us as I prepared our permanent residency docs. We had an easy situation as parents of a Argentina-born child, but thanks in part to the advance emails to migraciones we had everything required in one appt for me, my wife and US-born daughter. (we completed about two years ago for some context of timing of process). Note: I always sent my emails to migraciones from a generic email address and did not cite my personal case information (full, name, passport, address) until it was necessary as we were "irregular" at the time. I didn't want the writing to be turned around against me. Perhaps, unnecessary, but it made me feel better.
So if you want to test the waters solo...
Here are all the delegations and contact info. Hours, Phone, Fax, Email, etc.