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Others who have more direct personal experience dealing with these things should hopefully give you some specific advice on what to do next, but I have a few questions that may help people help you, by providing fuller information.
First, when you say you have evidence that the deferrals were accepted, what exactly do you have? Is it in writing? Were there stated terms and conditions that they agreed to, in writing? And is there anything you were supposed to do by certain dates and times?
Second, when you say that they have acknowledged this, do you have that in writing? And if so, what do they say they are doing next? Have they told you what their plan is?
I think the ideal thing is if they can just go update their reporting from their end to mark your loans as having been paid as agreed, that should eliminate all the late payments if they do that. And then you would presumably be able to challenge the collections on the basis that you were never late--and they might be able to do that as well. But for these steps I think others here with more direct personal experience can probably give you some specific advice.
In any case I think you should start by trying to resolve this through the lenders themselves, and see if they will fix it. If they won't, then you would move on to disputing it through the credit bureaus--at which point you're going to need all the documented evidence you can get to make a strong case.
Ah great thinking! I didn't even consider the actual AMOUNTS, I just was worried about the negative reporting. However, you are right... the amounts matter too! What a pain in the behind student loans are. Half of mine are serviced by one company and the other half are serviced by another. I suppose the positive with this is that half of them were NOT messed up and were reported accurately, so at least there is that! It is just a bit confusing to me to look at my credit report and see SO MANY loans, all listed a variety of ways because they were bought / traded / whatever'ed multiple times leading up to this point. I think I need a spreadsheet or something to track everything.