If your list of stipulations includes basic reiterations of generally-applicable site rules, like GS/BS, not just links, and so forth, those are generally redundant and tend to produce bad results. After all, if the question needs those, then so do most questions, and the result of that is a bunch of extra noise. Instead, site rules need to be spread through comments, the help center, meta, and so forth. There is a possible exception for posts that have proven to be remarkably good bad-answer magnets, which can get a post notice or similar to discourage them. (Or can even be closed.) Still, better site culture would reduce the frequency of those, and that's what we should focus on.
If, on the other hand, it's highly-specific criteria that define your situation — including potential specific classes of solutions that won't work — then that's an excellent part of the question!
Your first question has these stipulations:
Answers should be based on experience, not conjecture. That is, I'm looking for a solution that proved to be objectively effective for whichever person employed it or experienced it at their game table. In addition, answers should not depend on altering the seating order of the players. Assume the seating order is arbitrary and fixed for the entire session.
Note that answers suggesting alternative methods for tracking standard initiative (whether they be tents, cards, placards, lists, or so on) do not actually answer the question I am asking. Correct answers to this question must establish a house-rule for calculating initiative in a non-standard fashion, not just for recording standard initiative using a different medium.
I've struck through the restatement of GS/BS. All responsible answerers and voters on the site need to be aware of that as a basic fact of site use, so tying it to this particular question, as though other questions do not need the same consideration, is noise, and may tend to even encourage ignoring GS/BS when there is no explicit disclaimer in the question! The bolded section is an excellent, well-stated limitation that defines the question better.
The second paragraph is a bit more problematic; RPG has a long history of frame challenges, and outright saying "this type of answer is NAA" isn't really the way to handle those. Instead, like the earlier restriction, it should be phrased in a way that makes the problem statement clearer without assuming anything about the answers.
I think this deserves a bit more emphasis. Questions should not assume things about the answers. That's for the answerers to do, and the voters to judge. They should state the problem, and let the ones who are trying to solve it do the solving!
Since this paragraph is just restating what the title and bolded question summary have already said, I don't think it's necessary to include at all.
Cite rules or authoritative rulings if available.
Otherwise, recommend house-rulings which have been demonstrated to
be feasible and balanced through actual use at a table.
Answers should not...
Suggest untested or hypothetical house-rulings.
- Suggest adding features such as the find steed spell to the player character.
- Suggest removing the Shadow Blend feature entirely or nerfing it beyond recognition.
Suggest that I am wrong to want to allow a shadow mastiff as a mount.
Suggest that I just use the naive answer described above, which I already rejected.
Here again, there are restatements of basic rules like GS/BS, as well as restatements that, in fact, the problem statement described is the one intended. Voters and answerers are not stupid; a reasonably-well-written question will generally get upvoted answers that do actually respect the boundaries stated… or that give extremely sound reasons for not doing so, which are even more valuable. If you got an extremely cogent argument for why, say, shadow mastiffs are a surprisingly bad choice for reasons you had not considered, it is not beyond reason that you, or someone else with a similar problem, might be convinced and decide to do something else.
It's not clear why find steed is a problem. That should be explained, if possible, rather than flatly stated. Similarly, the reasons for wanting specifically Shadow Blend could be expanded on a bit more in cases there's a better way to accomplish those.