Personally I really dislike eggbutts and loose rings, but I see plenty of full cheeks that go unpenalized. You almost never see eggbutts or loose rings in the hunters, but top horses such as Casallo go in full cheeks. I feel like Dees, eggbutts and loose rings are so similar that I would go for the Dee at shows to be purely asthetic and maybe a loose ring or eggbutt at home.
If you find 8 spots the judge isn't going to care if you have an eggbutt or a D-ring. If you don't find 8 spots the judge is going to have much more to penalize you for than having an eggbutt and not a D-ring.
The only bits you would be penalized for are what the judge considers "unconventional tack." There is some debate about whether some judges would penalize for a pelham. I showed my jumper in the 3ft hunters in a pelham and never felt penalized for it - but we either had amazing rounds or not so great ones.
I once showed in a loose ring (my normally schooling bit for that horse) instead of the slow twist D I had used in the past. My trainer said that it could have the potential to knock me down (say, from 1st to 3rd). We went with it anyway because he was going much better in it and the goal for the day was to have him have solid, positive trips in the ring, not win. If I had continued to show him (oh, law school getting in the way), I would have spent time looking for another option.
Find 8 nice distances, keep a good consistent rhythm, have a neat and tidy appearance, and you will be good to go.
All of the bits you have listed above are conventional. If you used a kimberwick, or some of the Mylers with the hooks/chains then you may get penalized. Other than that, I doubt a judge would really care if you were in a D, eggbutt, loose ring, full cheek, or a pelham.
I've shown in all the bits you listed and have never felt penalized for my horse's bit. I get penalized when I can't see a distance, miss a lead change, or knock a rail.
I showed my mare in a loose ring on the A circuit. It didn't appear to harm us at all. We pinned many top placings, and I don't believe for a moment we would have come out any better in a D-ring. I showed a lovely QH mare a couple weeks ago in an eggbutt. We were 2nd, 2nd, 1st, and reserve champion. I don't think having her in a D would have changed a thing.
Neither showed in a martingale either. I feel like such a rebel, lol.
I do believe there may be some differences between showing in a pelham and showing in a snaffle however.