Hmmm, I'm a little confused, I was under the impression that you couldn't run more than a 31" tire without some kind of a lift? (I might be wrong as I'm still new to this, but I can find some citations if required)
it depends on your application.
AEV has a kit that raises your fenders, and you can run a 34" tire on a stock jeep.
I have never tried this, but I think you could probably run a 32.5" (ish) tire on your jeep provided it isnt over 10" wide on your stock rims, but you may have problems as well depending on where you go and how you drive it...and not many like the look of pizza cutters on a jeep. If you are handy with a utility knife, you could probably go wider. This little statement is vague and up to interpretation, and can (and likely will) be argued successfully.
I currently have a set of 32x11.5's on my stock ride height tj (with 12x kms) without rubbing or any complications (sway bar connected), and I know I would be able to fit a 33x12.5 on and I wont have issues, however this is mainly due to the wheels, and the offset of those wheels and the flares I am running. My net gain is 1" of ground clearance and my trade off is worse fuel economy then stock and a higher rotating mass which has a negative effect on component longevity.
Bill is referenced on this site that the biggest tire you should run stock is the tire you have as seen
here.
I agree, however there are factors at play here as well. For example, IMHO it is impossible to say that 31x10.5's will fit all jeeps because from stock not all jeeps had the same wheels or offsets. Case in point, the "gambler" 15x8 wheels had a different offset then the Canyon and the Ravine 15x8's, however (off the top of my head) I believe the gambler has the same offset as your 16x8 rubi wheels...and so on...and that does not touch on the topic of the varieties of 15x7 wheels from stock.
but back to the OP, I made the same error, I wanted a small lift, bought a 2" BB, read, was alarmed, read some more, and sold what I bought. 99% of the time, cheap = poor quality junk.
Buy this and buy some used tires in a 31 or 32" variety and you will be off to a good start......
-=edit=-
I re-read your original post, what do you mean by "progressive approach"? what is your goal? That 2" OME kit may not be worth it..I posted that thinking that you wanted to lift your LJ 2" total...but that was perhaps an incorrect assumption on my part..