I have an old treadle base very similar to this.
I have seen lots of guys try to set up treadle operated tools, none of them very successful.
Piercing cloth with a pinpoint? Requires torque, and a treadle can sew 8 layers of Levis. I have seen it many times. All the women I knew used treadles for years. I pretty much worked on them all, over time.
But other jobs just require too much torque. Treadle tools for larger jobs than sewing used much larger heavier flywheels.
The most successful lathe I know about was made by Larry Holland, from Washington state.
His has a 4 foot flywheel, 5 inches thick!
You need mass on your side if you are going to treadle though wood.
I would expect a 3 foot flywheel about 3" thick (cast cement is popular in the modern world) would do a jigsaw well.
yours Scott