No, we really don’t. Google scholar search for “neutral mutation”: 19,400 hits; for “effectively neutral mutation”: 88 hits – 22 hits of them in last decade, and many of those are just to the title of an earlier paper by Kimura that’s being referenced. For “neutral mutations” vs “effectively neutral mutations”, it’s 14,700 vs 371.
Mutations that are neutral enough for all practical purposes are believed to exist.
All you’re showing is that a lot of papers are unfortunately vague, or they’re just using the unqualified term “neutral” as a shorthand, knowing their audience will understand they really mean “effectively neutral”.
“Neutral enough” is not “strictly neutral”. “Neutral enough” can accumulate. Strictly neutral has no accumulated weight regardless. You know all this.
No one has established that most mutations are damaging. You’ve asserted it many times, and we’ve pointed out to you that no one has ever established it. You address this by repeating the assertion, sometimes by quoting papers that also don’t establish it.
In any case, you asked about junk DNA. Since we know the origin of much/most junk DNA, and that origin implies no optimization of the sequence involved, that means almost all mutations in that sequence should have zero net effect.
I actually did laugh out loud at your response. I am their audience, and you’re trying to tell me what I understand by what they’re writing. Just no – you’re wrong.
No, neutral enough can’t accumulate, because there’s no excess of slightly neutral mutations. You know this, or you should since you’ve been told often enough.
I legitimately cannot make out what you’re implying. Are you saying there’s a third type of neutral mutation besides effectively and strictly neutral? I know you’re the audience, and unless I’ve mistaken you’ve agreed, just as Dr Felsenstein has, that there are no strictly neutral mutations. That only leaves us with effectively neutral.
You’re saying they all balance each other out perfectly?
You are so very confused. Junk DNA has no function (or at least the specific sequence has no function). If you change it, it doesn’t break anything. There’s no information stored in it. The only thing that might happen when it mutates is that DNA replication might become slightly more or less efficient. Since junk DNA was never optimized for efficiency in the first place, it becomes more efficient at the same rate it becomes less efficient.
Again, you’ve been told this over and over. Try this: stop quoting your favorite papers and stop typing, and try to understand what biologists are telling you.
This is just like the monkey with the typewriter. Let’s say it has no information. That doesn’t imply that changes are just as likely to be beneficial as deleterious. Building information is hard work. It’s not likely to happen by chance. That’s why it takes intelligence to write novels, papers, blueprints, etc. We don’t expect that throwing random stuff together will be “just as likely” to help as hurt. It almost never helps, regardless. GE does not depend upon the assumption of starting with perfection.
No, I’m saying we aren’t mentally adding ‘effectively’ to ‘neutral’ every time we hear it because it doesn’t matter.
Yes, let’s. Let’s say I hand you a page of meaningless gibberish, typed by a monkey. That’s what junk DNA is. Now start making random changes to it. Do the changes make it more or less meaningful?
I wish I had a dollar for every time a Creationist makes the false claim evolution works just by chance. A dollar for every time they deliberately omit the effects of feedback from selection in making and saving positive changes. I’d pay off the national debt and still have enough left to fund the NASA Mars missions. 
Parts of the genome are not being removed. That’s not how it works. Variation can be removed through selection, but there are still alleles for each of those genes. Phenotype is still directly tied to the sequence of those alleles, and according to you those differences between sequence among alleles should be mostly deleterious. Selection doesn’t remove junk DNA, either.
Let’s extend the analogy. Letters take different amounts of toner to print. So each time you change a letter, you’re changing the printing cost of the page slightly. Now go back to making random changes to your page of gibberish: do you think that as you make change after change, the cost of printing the page will steadily mount?
Who has done so? Please produce a single quote to support your claim of what others are allegedly suggesting.
How do you explain the false and very large elision you’ve made here?
Why are so many creationists apparently unable to understand that noncoding does not mean junk?
Or are you just pretending not to understand, Paul?
The more gibberish you have, the greater the cost obviously, with no benefit since there’s no information. As you make random changes (not really random, but actually biased changes), the information content does not increase. It remains gibberish. Anything you add increases cost to print, which is deleterious. I don’t see much chance for anything beneficial in this scenario.
How so? Do most mutations increase the size of the genome?
No, I didn’t say they do. But each letter costs toner.
Who said anything about more gibberish? Stick with the analogy: you start with one page of gibberish and make changes to it. Does either the information content or printing cost of the page change systematically over time? It’s a yes or no question.
So did the letter it replaced. So does the cost change?
Junk DNA is already gibberish. Changing some gibberish for some different gibberish does not increase gibberish.
There are not enough facepalms for this in all possible worlds.