I want to make sure I'm understanding this correctly: you want to lift the car with the screw jacks pictured above? Doesn't the square platform also turn with the threaded shaft? It appears that the two halves thread together with the operator turning the platform to adjust the height, then locking it in place with a jam nut. That won't work if the body is secured in a channel that's part of the platform unless you twist the base to lift. I think.
You may be creating extra work in the name of safety as well, but that's ok. Shop safety is vastly underrated. I didn't disconnect much if anything when doing the Elk mounts, and don't see a big benefit to removing the bumpers aside from doing the required patchwork. The coiled brake lines have plenty of flex to allow the body to rise the required amount above stock height (about 1/8" worked), and I might've even left the steering shaft connected as well. Placing wood between the body and frame provides an opportunity for things to get jammed and would also put your fingers in the danger zone more often, but I completely understand where you're coming from. I'm a risk-taker and trusted the jack to not blow out but also only removed one bushing at a time so the body could never fall anyway.
My recommendation is to use a 2.5 or 3 ton hydraulic floor jack if possible, with a long grooved 2x4 on top, and using 2 jacks would be better.
Or using a H.F. crossbeam between the single jack & lumber would provide additional stability as well as height adjustability at each end. I also understand that buying the jack and beam could be about $300 though. I used a single jack and board but can't recommend the beam enough now that I have one.