The Small picture on the steam page actually contains a working catapult. Just a few blocks of height can provide sufficient leverage, potentially with a weighted end to pull it down. You can add the weight to a decoupler bound to the same key you use to contract the strings, to provide more velocity for a single shot version. The reason to use the regular hinge is that you need that freedom of movement; if it automatically explodes or falls apart without steering, it's just not a terrible feasible design.
Of course it's going to tilt towards the upper arm, but that's not a problem. If anything, it's going to give you more impulse for when you send your payload flying. It's like saying "I have to pull my arm back to throw a ball!".
If you replace your pistons with two wooden blocks with a hinge on top, it should work with some finagling.