Tensile testers are fun, I've worked a lot with them. Most fun was drawing fibre reinforced epoxy pieces, they make a nice mess when they break.
One thing you have to look into is your pressure sensor. Tensile testers don't measure pressure, they measure force. We used to call these things "load cells" and they produce a reading in newton rather than PSI (which is force per area). PSI, or better: Pascal which is the SI unit, is force per area, and the area depends on the object that's tested. Therefore pressure doesn't make sense for a tensile tester.
Instead of a linear transducer, you can also use the screws that move your table to measure distance (at least I assume you go that way with the machine itself). Mechanical limit switches, after that it's a matter of counting (fractions of) rotation and you know exactly how much your table has moved. The speed of the rotation sets the speed of movement of the table. After all you don't normally care as much as where the table is, as you care about how much and how fast it moves.