To thine own self be true
There's a bit of a subtle twist to the scenario you describe here...
A question is posted on one SE site (call it site A) and closed. It could be closed for a variety of reasons - from off-topic to simply not meeting site A's quality standards. [...] It also gets downvoted [...]
Another SE site (call it site B) would welcome this question: on B, it would be not only on-topic but also considered good quality [...]
Critically, the question in this scenario has not been well-received on the site where it was asked. Now, you can (and do) argue that it would be well-received on another site, but this is speculation - unless the question already exists there (and thus would be a duplicate if migrated), you're assuming that whatever problems afflict it on the site where it was posted wouldn't apply or would be easily mitigated elsewhere.
This is a totally understandable assumption, the sort of prediction I've personally made plenty of times myself and watched others make over the years... It has proven to be a routinely dangerous assumption and one that has personally cost me a tremendous amount of time and energy.
See, some folks really, really hate it when it looks like you're dumping trash on their site. Even if it's your site too. Even if your trash is attractive garbage art and you're simultaneously helping to pick up tons of litter every day. Something about the mindfulness of migrating a somewhat-problematic question is infuriating in a way that dozens of thoughtlessly-posted problematic questions are not.
Now, I generally recommend migration in cases where the voters or moderators have a good-faith reason to believe that the question will be successful. This can include questions that are poorly-received, as long as their only fault is that they were asked on the wrong site - for example, questions about the use of web applications asked on Super User, or remodeling a kitchen asked on Seasoned Advice.
But it can be difficult - not to mention time consuming - to defend a migration in cases where the folks migrating it feel that it is inherently problematic; that is to say, it stops being a "good faith" migration if the only reason you believe it'll do well elsewhere is that you hold a dim view of the ability of the folks "elsewhere" to moderate their own site. Ultimately then, this is a judgement call: as a voter or moderator, you are first and foremost accountable to your own conscience; if you can't look yourself in the mirror and defend an action, you have little hope of defending it to anyone else.
A Practical Approach
I skipped over a pretty big part of your question to get to the answer above, because I think understanding the often-complicated nature of how different sites relate to each other (and to themselves) is critical to understanding what comes next... But I tend to agree with this:
The alternative to getting it migrated, upvoted, and answered on B would be leaving it on A to rot away and be auto-deleted, which is no use to anyone, neither site nor the OP.
That's generally my philosophy as well, not just for migrations but also for editing: if you can salvage a question where the alternative is deletion, then you should try to do so when you see something of value - potentially going to more extreme lengths than would be prudent under other circumstances.
The critical factor there is that you see something of value, and are thus moved to expose the proverbial diamond in the rough. If you're just going through the motion to salvage a question you don't really see value in, then you're in danger of acting in bad faith, creating more work for others for no good reason.
So, what can you do in the scenario you describe?
Edit. This is almost always my first recommendation, and for good reason: you can easily waste days trying to explain the worth of a question to someone else when with a few minutes worth of editing you could just show them.
Note that if you're able to correct all of the defects in a given question it might end up being fine on the site where it was asked, your request for migration denied anyway - and that's still a success. But even if the edited question remains off-topic, you may at least render it attractive enough to allow others to champion it in good faith.
Answer. Obviously, this is impossible if the question is already closed, but if that's merely a likely outcome then posting an answer can help to establish your credentials as an expert on the topic, as well as someone with a vested interest in the fate of the question. Obviously, your answer needs to actually be good in order for this to matter; posting a downvoted answer on a downvoted question doesn't do anyone any favors.
Re-ask the question yourself. This is one of those techniques that's so obvious and boring, folks seem to easily forget about it: if you can't convince someone else to accept changes to their post, or ask it in the right place, or even return to the site... Then do it yourself.
There's a certain "put your money where your mouth is" aspect to this technique; obviously, you would never do this if you didn't believe there was some inherent value in the post, lest you sully your own reputation... But, we went over the whole "good faith" thing above already. Regardless, if you're sufficiently moved to put a question under your own name, you're taking a bit of a gamble: if you were correct and the value becomes apparent in the right light with the right cut, then you get to collect the rewards; if you were wrong, you earn the inevitable payment for that as well.