I worked for Geokon for a while and while I cant share trade secrets of their design, I may be able to point you in the right direction and point out issues we ran into with loadcell design.
The biggest piece of information is if the measured output can be scaled to a linear fit and that it holds zero under various conditions. The ring that most loadcells are has to be of a metal or material that will expand under pressure and contract when pressure is released from it and not drift from its zero. (* This is harder than it sounds, as for most materials yield after repeated pressure applications to where your zero will shift and it will have to be recalibrated )
If this fabric was looped around a chunk of rubber which generally will expand out and contract back to its original form, you may be able to make a low pressure loadcell with little difficulty, however you will need to make precise measurements under stepped pressures and then plug your data in to find the linear fit of the curve to be able to display an output pressure based on the load and have it correct.
You also have to worry about environmental factors that may skew the data such as humidity and temperature with temperature requiring a calculated offset to measure correctly between say 32F and 100F as for rubber is more firm when chilled. This is less of a problem with using a metal ring, however it is part of the calculation when precision is important.
I also worked with Strain Gauges at Geokon and while here I also can not share specifics, you should be able to use this fabric as a strain gauge setup. The Strain Gauges that I worked with were mainly Transducers though, where piano wire was at the core of a tube with 2 ends that were attached with this wire. When their was tension on this strain gauge it would add tension to the piano wire and the coil that plucked the piano wire via a magnetic pulse was also used to measure the vibration of the piano wire which has a frequency change when tension is added, this then can be used to calculate the amount of tension as long as the wire is not over ranged. When over ranged the wire stretches and it has to be re calibrated for a new zero or thrown away if damaged beyond repair.
You will need to run tests on this fabric to know how much tension it can take before it loses its zero and then you will know how much strain can be applied on it. If the range is limited, you can modify its range as how much strain it can handle by adding something else parallel to it that will add strain resistance so that the fabric itself is not the only connection between ( A ) your fixed surface, and ( B ) the movable end that can extend ever so slightly away from ( A ) to apply strain to the fabric and get measurement from.
So if you have any questions, I will help out the best I can, but I cant share trade secrets that I know of Geokon which include metals used and specifics of how the measurements are computed and scaled. Everything contained up to here is common knowledge with customers of Geokon's products. More information can be found here
www.geokon.com