A good, quality .338LM rated suppressor is probably gonna cost you more than $1k. The only one on your list I'm familiar with is the Elite Iron, and probably the only one that makes a solid .338LM can comparable to TBAC or other, high quality mfg.'s on there.
I have the Elite Iron .338 and .50 cans. I have not shot the .338, I don't have the rifle yet. Anyway, Elite builds quality cans that use a similar mount to the TBAC (thread over brake) so it locks down tight. It's well made and it's not all that heavy considering it's a solid SS can. The can itself is around a foot long, but the brake goes over the barrel for a couple inches so it takes some of the length down. Any color Cerakote. Elite also does some great custom work. Dale is the owner and he's an honest guy, if you have any questions about what it can and can't do (and recommendations for his competition even) then call him up and ask him. Excellent CS, what little of it I've needed. He keeps the costs down by using 316SS, and did I mention he's honest? Since cans are easy to make and he uses mainly 316SS, it means they cost less, in particular the .338 and .50 cans, compared to competition. They're inexpensive, not cheap.
I don't think some of the ones you listed can handle .338LM, I'd check to be sure it can handle the load you intend on using. The 9mm cans that mention .338 for instance, are generally referring to .338 Whisper and the like.
Sico is a company I like, but I didn't know they made a full on .338 can... If so, they'd definitely be on my list. Love the Omega 9k and Saker.
Are you using direct thread? AAC looks like they are cleaning out, possibly "going out of business" (they were bought out by Remington, so...). They have a lot of sales. I would have to warn you to stay away from their QD mounts, though almost everyone who actually owns a 90T mount swears by it. Their cans are nice though, I can't say anything bad about their performance and actually like the SDN6 for .300BLK, if only the mount were better. So if you buy a direct thread, AAC is worth considering, especially if you can get 'em to sell it to you for less. The 90T may be worth considering too, I don't know. I heard their bigger cans were pretty nice and know they used to be pretty expensive.
You said TBAC is out of your price range, but I'd say to save up a bit if you want one of those, and I think you probably do... If you don't mind the extra bit of weight, the Elite Iron will do you fine. If you want the weight savings you get from titanium, TBAC is THE one to consider. I have their .30's and a 6.5 but I've heard others laud the .338. They're great for accuracy, come in all colors and use a thread over brake and have an honest owner that does good work, all like Elite. Given how much a can costs and the wait, etc., it's worth it to get what you want the first time.
Stay away from gimmicks, promises (too good to be true, generally) cans and companies with a bad following online. Stick with trued and tested designs by quality oriented mfg.'s that are honest.
Besides, you can always buy the can, and then later, pay the tax stamp and your dealer his cut when it gets here.