This is absolutely correct, with one minor correction. You aren't compressing the bar, you're twisting it, as PeteN95 noted.
Also correct.
psrivats, that is indeed the formula used. However, it does not require a conversion factor depending on units. There are only two units used in the equation - force and distance. As long as consistent units are used, it will yield a correct result. For instance, for US units, use pounds for the force unit and inches for all distance units, and you're good to go. Typically, the value for shear modulus is 11,500,000 pounds per square inch. That's close enough for most steel and steel alloys. Actual values vary a bit, but that value will be within 2-3% of actual values.
Correct again.
On a TJ, no, it doesn't change enough to matter (continue reading for more on that.)
Agreed, but there is a way to get close on the first cut (continue reading...)
Basically true. One could argue that a progressively-wound or multi-rate spring won't follow that rule, but the formula psrivats posted doesn't address helix angle because, in practice, it doesn't matter. The spring won't be stable if the coils are far enough apart for that to matter. It will bow severely when compressed.
True again
I've attached a spreadsheet I put together this evening to help the OP determine how much to cut off. Unfortunately, you'll need Microsoft Excel to open it. I'm not savvy enough to create a Google version of that so that anyone can look at it, so if someone wants to do that, knock yourself out. Note - I don't have data on the Zone springs. I do have my RockJock CE-9132F springs sitting on the floor of my shop, so I measured those and put the values in for them. I then tweaked the amount cut off until I got close to a 14" installed length, which I believe is a 2" lift (someone correct me if I'm wrong, please). It comes out to 2.75" cut off, and the spring rate increases from 136 lb/in to 155 lb/in (a 14% increase). As has been discussed on this forum many times, spring rate on a TJ is just not a factor in ride quality. A 14% increase won't matter. Of course, the RockJock spring is dual rate, and I didn't have time to actually verify that for the spreadsheet calculations, but I don't think it'll matter much; however, I could be wrong, so be careful if you actually use this on a multi-rate or progressive spring like the RockJock springs. I could take a look at how the calculations turn out for a dual-rate spring, but I don't have time tonight. Here's a screen shot of the spreadsheet:
View attachment 446586
The way the spreadsheet works, you enter the yellow highlighted cells, and the other cells get calculated for you. If the OP decides to use this, he'll need to replace all yellow cells with measurements from his springs, with the exception of the Shear Modulus and the Stock Spring Installed Length because those won't vary from spring to spring. Also, spring rates in practice can have wide variations, so I'd suggest that you cut less off at first because it's tough to put part of a coil back once you cut it off!
Final caveat - I have designed too many valve springs and suspension springs in my previous career to count, and I even wrote the specification manual for suspension springs at one company I worked for. However, as a human, I'm prone to mistakes (especially at this age). I can't guarantee that this spreadsheet is correct, so use it at your own risk, please! If you do find an error, let me know and I'll post a correction.
