When you sight read a piece or look at a piece, do you first break it down as to which key it is in and which modulation etc. etc...? How do you learn to do that fast? Do you know of any simple not-too-hard tango duo pieces? I would love to obtain a copy of your take on Piazzolla, but currently, it is not available, right?
The more you sight read, the easier it will be. As a child, I would loan piles of music from the library - whatever interested me really - and play through it all at home. At Juilliard, I often checked out the maximum number of items from the library (45 items) because I was curious to read through music unfamiliar to me. The piano repertoire is like a giant treasure trove - there is so much good stuff out there, and the only way to become familiar with it is by listening or sight reading.
I'd recommend you start with what feels comfortable and go from there! Buy an "easy" classics book, or read through the Mozart sonatas, move on to the Chopin waltzes, etc. Gradually the process will become easier. For me, it is not a matter of analysis (keys, modulation, etc.) but recognizing visual patterns in the music (arpeggio figurations, chords, stylistic tendencies, etc.).
As for your other questions: I'm not familiar with any tango pieces for piano/four-hands, although I'm sure there must be something out there. Keep searching! And you are correct, my arrangement of Piazzolla's is not available yet.