(apologies for the very delayed response, but i wanted to answer in case you or others could still get something out of it)
that orange bottle tanning solution ("deer hunter & trapper's hide tanning formula") is awful both as a product and for the directions it gives, and i strongly advise against using it. based on my and others' experiences with it, i'm not convinced it actually is a tanning agent at all. it's what i started out using as many folks do since it's so readily available and makes the process seem easy, but the results were never good. when i got more experience and went back to rework some of the pelts i used it on- because they always turned out stiff- upon rehydration they started shedding like crazy and when i began thinning them down some, the skin under the surface was reddish and raw- not tanned. most were squirrels so it wasn't a case of them being too greasy or thick skinned for the tan to have worked properly, i followed the instructions exactly and it just did not actually tan them. i've heard similar issues and more countless times from others who have used that orange bottle stuff.
but even if it was a decent tanning agent, the directions it gives you will not result in a proper tan regardless. one of the main issues, as your question implies, is the lack of a pickling step. after the salting stage it tells you to soak the hide in salt water for a few minutes to several hours- presumably the rehydration step- and then thin down the skin. it's pretty much asking for slippage here, instructing you to take a wet, raw skin and spend time trying to thin in down. raw/unpickled skins are very difficult to actually shave down even with a fleshing machine, and you're really not going to be able to be thorough enough on most critters in the timeframe you'd need to be done with it before it begins to slip (especially as a beginner and with no fancy equipment). pickling is a crucial step in the tanning process not only because it breaks down untannable proteins within the skin to prepare it for tanning, but it also toughens up the skin/changes the texture to allow you to shave it much more easily, as well as preserves and stabilizes it so you can spend as much time as you need to on shaving it.
the next major issue with the directions is the lack of a proper degreasing step. fully and completely degreasing the skin is imperative for any tanning agent to work, so you really need to get it right, but the orange bottle does not tell you how. what it tells you to do is wash the hide with dish soap, or if it's a very greasy skin like raccoon or bear, wash it twice. problem is, you could wash a raccoon ten times with dish soap and it's not going to fully degrease that thing- especially if you could only do a rushed shaving job because the instructions put you in a race against time trying to shave a raw skin before it spoils. very lean critters like squirrel or deer can be fine with just a wash in dish soap, but for most furbearers like coyote, fox, mink, opossum, raccoon, etc, that won't cut it. in order to get degreased properly these animals need to be thoroughly shaved, and soaked in a solvent-based taxidermy degreaser. as a surfactant, dish soap is just not effective in dissolving the grease deep within the skin.
you can get a decently preserved pelt with the orange bottle stuff if you follow the proper tanning procedure instead of its instructions (flesh, salt, rehydrate, pickle, shave, degrease, neutralize, apply tan). but at that point if you're already buying the extra supplies to do that you might as well just get the trubond tanning kit instead, which has a very high quality tanning formula and much better instructions. the orange bottle formula itself just not good even when used right. i reworked a squirrel i 'tanned' with the orange bottle by just oiling it with trubond 1000B and the difference in how soft it turned out was night and day. even on its own without the proper tanning process, the trubond worked so much better. i stopped using the orange bottle and never looked back. even with my very limited experience level when i switched, my pelts immediately began turning out SO much better when i used trubond and followed their instructions.
i'm sorry i couldn't help with your bobcat in time! if you happen to see this i would be very curious to know how it turned out