Txisalive:
The lates are accurate as reported, which is why they will not be removed through a dispute. The proven isn't there credit bureau, it's your servicer. I'm guessing you've talked with them multiple times and have not gotten a solution.
You're absolutely correct. When you turn in a new IDR application or recertify your loans should be put on administrative forbearance when they were received. I'm not sure if there are any specific rules about this but it's pretty standard. Additionally they seem to be taking longer than the standard one month to process our IDR applications often (fastest is the online application with the IRS link). I'm unsure if it would have been up to you to ask for them to continue the forbearances into the second month.
My advice is to go with your gut and put this all on them. Believe that they 100% should have done these things and that it's their fault for not putting you in the forbearance and the resulting marks on your credit report. Take this conviction and put it into a narrative, then file a complaint with the Ombudsman first, then there Consumer Financial Protection Bureau. I say it this way because I've found that if you give the servicer any wiggle room, they will take it. Be ready to submit an supporting documentation (including bills, your IDR application, communication logs, etc. ) and then some. An acceptable response would be for them to correct the lates and your credit report.
Good luck!