- Use your downvotes
- Be consistent
- Leave clear comments with meta links to policy, and try to give concrete suggestions for improvement
In more detail...
(sorry, this ended up way longer than I expected!)
1. Make it less rewarding to post bad answers
I'll start out by saying I don't think there's a good way to tell another user "I think your answers are of such poor quality that they're hurting the site." The bigger problem is that they still get rewarded for posting these types of answers - if they were always downvoted and deleted, you wouldn't need to comment for them to realize the answers are poor for IPS.
Instead, these answers often get upvotes. I've even seen flagged answers without any downvotes. No consequences = not much of an incentive to edit and improve. We need to downvote bad answers.
2. Consistency is key
If it's consistently less rewarding to post "try this" and un-backed-up answers, there will be less of them to begin with, and perhaps these users will be more incentivized to improve their posts.
It's also important to be consistent in enforcing standards. A common complaint about IPS is that it seems arbitrary what's ok and what's not. When Alice's answer gets commented on and flagged/deleted but Bob's doesn't, and they don't see a clear reason or categorical difference between the two, it looks like we're being inconsistent. I suspect some users think "50/50 it sticks around and I keep the rep, might as well post it and see what happens, right?"
On a practical note, critically reviewing a post takes non-negligible amounts of time, so sometimes answers do fall through the cracks - flagging is the only way to guarantee a post gets looked at. So more users flagging and reviewing should help with consistent enforcement as well. (I think chat has been pretty helpful for getting more users aware of policies, people seem to discuss that sort of thing fairly regularly.)
3. Leave clear comments
When asking for improvements because you think it falls short of some policy, link to that policy. Don't wait for the OP to ask/argue about it. Fortunately we have a some handy posts (soon to be) under faq and faq-proposed (I frequently link to the relevant section of How Do I Write a Good Answer? when commenting).
Include context and be specific. For instance, with backup - they probably think everything is common sense, or that it has adequate explanation already. So say what specifically tripped your "insufficient backup" alarm, and if you can, suggest what sort of information would be sufficient to fix it, e.g.:
Could you  to explain why [unsupported statement]? How does this account for [complication in OP's situation]? Has this worked for you before in a similar situation, if so could you explain how that went?
The answerer can still choose to ignore it, but now it's very clear what the problem is - to them, newer users, and reviewers. It's also harder to argue with - "sufficient backup" can be a bit nebulous, but "has reference for statement X" much less so.
A bit of a side note but I feel it should be said... I'm a software engineer, I work with a lot of other engineers, we can be quite good at nit-picking based on what's more-or-less personal preferences and framing it as an objective concern (cough code style)... Here, it might be tempting to "rules-lawyer" answers you don't like and keep asking for backup and such on posts you disagree with. But doing that is liable to make people feel singled out, or that only certain points of view are acceptable (or unacceptable) - especially when other answers do not appear subject to the same level of scrutiny.
That's no good for building community, and for that matter, looks intimidating to newbies who may be deciding whether or not to stick around. So personally, I do some introspection while moderating, making sure I'm not simply using "You need to provide backup for X" as a proxy for "I don't like this answer and I need a plausible reason to delete it". (If I've left similar comments under other answers I do agree with, that's an easy call. Other times, I leave it with a downvote and flag and wait to see what review thinks, or ask in chat for a second opinion. I also try to review any other answers while I'm there as well.)
I'm starting to see "mediocre" and downvoted answers as a good sign for the site, personally. It means the bar isn't impossibly high. Not every answer has to be a soul-baring thesis, and it's useful to know that even though that worked for user1234 that one time, most people still think it's a bad idea.
On "Meta is Murder"
That phrase is from a blog post by Jeff Atwood. It's pretty well summed up by the last bit:
So sure, get meta when it makes sense to. But do be aware of what percentage of the time you're spending on meta. And consider: how is progress made in the world? By sitting around and debating the process of how things are done ad nauseam? Or by, y'know ... doing stuff?
Allocate your time accordingly.
It'll be a lot easier to convince folks that IPS policies are good and useful if we are generating high-quality answers while following them. We lost a lot of traffic to HNQ; if we're spending a lot of time picking apart the (relatively) few posts we still get because policy and not posting our own, better ones, it's going to seem like IPS "power users" are more focused on enforcing rules than producing helpful content.
Ultimately, I think the most powerful argument to convince people they ought to change their answer style will be to lead by example - get out there and show 'em how it's done ;)