I assume that you want to state the following: Some people are complaining and you would like them to stop.
Let’s phrase this as a typically arranged conditional clause first:
If everybody stopped complaining, I would appreciate this.
This is a typical second conditional, using the past subjunctive (stopped) for the condition and the conditional mood (would appreciate) for the consequence. A second conditional here indicates that you do not actually expect everybody to stop complaining right now, i.e., the condition is hypothetical.
Invert this to:
I would appreciate it if everybody stopped complaining.
The cleft is now added on top of this leaving the moods untouched, even if there is no analogous non-cleft construction (“[…] is if everybody stopped complaining”):
What I would appreciate is if everybody stopped complaining.
Add a few details to this and you get your final sentence.
What I'd really appreciate right now is that everybody would stop complaining about it.
What I'd really appreciate right now is that everybody stopped complaining about it.
Using that instead of if implies that the second part of the sentence actually happened or would happen (given some other condition).
Let’s first look at your second suggestion. Here, that implies that everybody actually stopped complaining (past tense, not past subjunctive). This would only make sense if another condition outside of the sentence causes the conditional mood in the first part, e.g.:
I left this company for good last year. But if I were still a member, what I would really appreciate would be the fact that everybody finally stopped complaining after the new CEO took over and offered substantial stock options.
The first example with would can work similarly, just that the second part (“everybody would stop complaining”) needs to be tied to the same condition, e.g.:
I left this company for good last year. But if I were still a member, what I would really appreciate would be the fact that everybody would stop complaining about my hair colour, since I changed it yesterday and everyone in town has had nothing but good things to say about it.