EDIT:
I think this is important for a couple reasons:
The strict nature of the rules, and the brutal hand of the mods in this subreddit have no doubt been integral to the stunning success of this sub.
That being said, I feel like integrity can be maintained with the following changes to the rules:
And, in order to keep things under control, the following limitations can be placed upon the two new types of allowed posts
A anecdotes and speculation must be labeled as such by the submitter of the comment. (ie unnmarked speculation would be subject to the same deletion policy that currently exists)
Speculative posts must be supported by evidence in the form of references and/or a cohesive logical argument and justification for lack of histiographical standards. (that is, they must answer why their answer lacks the level of evidence of first class answers).
Anecdotal comments at the top level are only allowed if there are no other similar anecdotes at the top level; otherwise they must be a child of the first similar anecdote.
Any measure which allows anecdotes and speculation will result in a rapid increase of them. Marking them will not abate that and, given that a lot of posters seem to not read the rules as it is, we can infer that anecdotes, speculation, and the inevitable jokes, will rapidly increase. It will mean a shit ton more work for mods, and it will lead to more deleted comment graveyards, not less. Voting has not proven an effective counter-measure. I can tell you as a medievalist that crap gets voted to the top as it is.
I would also counsel another bit of caution. I am a flaired historian here, and while that doesn't mean much it does mean that I speak offline to a number of other historians here. Based on those conversations I can safely say that if your proposals went through many of us would simply abandon this sub, and it would discourage others from joining.
This sub represents not just 'history' but proposes to reflect (to some degree) a way to think about history. These are tightly wound together and unwinding them would actually miss the point of the sub. The proposition then is that it takes some effort to contribute according to a standard. And that's OK: standards aren't in their nature a negative. If someone is not willing to put in a modicum of effort in a sub they chose to visit and comment in, I don't think their comment is worth preserving.
Edit: added last paragraph, because it occurs to me that it's a point often over-looked.
Most of this is stuff that has been brought up at some point or other, and in the end, decided against.
Speaking here only as a user, who happens to be a mod, I'd like to make some observations on the feasibility, but don't take this as me speaking ex cathedra. Just as someone informed by the experience.
Some subset of comments that are currently being deleted will instead be marked by either "cogent speculation" or "personal anecdote"
This actually would require more of a judgment call on the part of the mod team than the current system. Having a binary "pass/fail" system, while it will have its faults and failures, is going to be far less confusing than having a middle grey area. On top of this, it is almost certain that a fair number of posts which are marked as such, instead of contributing to the discussion of the topic, will simply result in META discussion about whether marking the comment as such was justified.
This is best represented by our approach to the anecdotes rule currently. Some of the most painful deletions to make are often personal anecdotes - I still complain about one I had to remove where I guy wrote about growing up in Northern Ireland during the troubles (If you are reading this man, I'M SORRY!). There is absolutely zero chance we would allow all anecdotes and speculation to stand with some sort of tag, and while it would be possible for us to evaluate each anecdote (or speculation) post on its own merits, this creates a myriad of problems.
It turns what is a simple "Yes/No" call into a judgement call "Does this anecdote meet whatever level we have decided they need to meet?"
The fact that it is possible an anecdote might stand will cause more people to post, as they think that theirs is worthy of inclusion, turning this into /r/AskReddit, and simply causing more deletions by the increase in overall volume of people posting them.
And on that note, the ones that are removed, when the poster disagrees with the removal, will lead to arguments about why a given anecdote deserved to stand.
So from a practical standpoint, as you can see, there are a few reasons why we don't want to start bending on the rules about anecdotes or speculation (the latter pretty much has the same pitfalls as anecdotes, from a practical standpoint). And for a more historigraphical discussion of why we are opposed to them, I would direct you here.
comments that are "marked" will always fall below unmarked posts using custom CSS
Putting aside the reasons we wouldn't want to allow these, even with some sort of marking, this also has a lot of problems. Mainly, it would be a massive undertaking in the CSS. /u/brigantus would literally kill which ever one of us suggested implementing this to him (each individual comment would need to be coded into the CSS I believe).
And then, even if we do put it in, many people browse on mobile, or turn of the CSS. These markings wouldn't be visible to them.
So the TL;DR is that it is a messy system to run, and a nearly impossible one to implement.
What idjet said, plus:
what you're proposing as a solution isn't actually a solution to the (perceived) problem. You have a problem with "content [which] is marginally-close to breaking/making the rules", and your solution is to loosen the rules to an extent which would open floodgates. If the problem you see is real, why not just have markers+css+burial+hide (don't know if all that's possible) for those posts under the current rules? Changing how edge cases are treated doesn't necessitate changing the rules.