The last time I took a long distance train in Argentina was in the late 70s, when the Argentine Railroads were still excellent... those were the days of the Full Pullmann service that my Grandfather used to take me on from Rufino (Santa Fe) to Buenos Aires. Outstanding seats, new linens white as snow pressed to perfection, staff with full dress uniform and a proper meal service.... today this all sounds like a tale from a time machine. All this was light years ago. As time passed, the entire Argentine railway system was basically nuked during the savage privatization at all costs of the 1990s and what remains today is in shambles, with service being mostly erratic and very very unreliable.
In this day & age... you have to be very, very, very cautious with train travel in Argentina, you need to do some heavy & intense expectations management and then some more. Sorry to rain on your parade.... did I say you need to manage expectations...?
I pray that Im wrong and since Im not a train type guy things have changed and service to Tucuman works fine... if this is the case, please, let there be someone here that can correct me.
Having said all the above... the only idea I can come up with, if you still want to consider doing this, is to contact a full service TA in Buenos Aires that should be able to assist you with booking whatever is out there.
Good luck, and please... if you do use the service do come back and report your experience.
Alex / Gaucho100K