As the datasheet says, the connector on the screen is the AXT434124. The counter connector is the

AXT334124. See also this link, according to which this is a suitable breakout board ("simple" 0.4 mm pitch to 2.54mm converter).

Using the schematic from this project as a base.

==

OK folks, sorry... it's proven to be too difficult for me. I'm posting this draft from half a year ago now, it holds a little more information. I finally chose for a display from a TI-83+ graphing calculator, which was easier. I might do a writeup on that.