I'm sorry to see you not getting far with this as I know that feeling myself. We wanted a furnished rental outside the city to enjoy a more relaxed life with our new baby and I contacted Reynolds and other big rental companies without much successs...and I speak Spanish. In the end a friend found us some lovely options in a barrio cerrado near her (Septiembre) in Escobar. They have large and small furnished houses for rent with communal facilities too. You can check out some options here for example:
http://propiedades.zonaprop.com.ar/...obar/ncZ24_opZtipo-operacion-alquiler_lnZ5117
I found the best opio0n is to drive to any barrio cerrado during a week day and talk to the office staff there rather than work via mail or phone. Trying to do it via the owners will be very difficult.
I know Escobar wasnt on your list of desired locations and maybe too outside the city but I thought I'd toss it in and hope things start going your way...