So I have a pretty close timeline to you, so hopefully this helps.
I made my last rehab payment on 16-Jan.
On the same day, I disputed the Fedloan tradelines (with all the late payments up to default) and the DOE tradelines (with all the charge off statuses since default).
Within 5 days, Fedloan completed the dispute and verified all reporting as accurate, which kept all the late payments.
Navient picked up the loans on 23-Jan.
On 1-Feb, DOE also completed the dispute and verified all the reporting as accurate, which basically kept the defaults showing.
On 8-Feb, the new Navient tradelines showed up with backdated open date and fresh payment history, but the old DOE tradelines were still showing defaulted with original balance. This dropped my score EX FICO 8 score 1 point.
On 9-Feb, the old DOE accounts were deleted from EX (TU and EQ not yet updated), and my EX FICO 8 score went up 66 points! Now I'm sitting at 678, and only thing holding me down is the late SL payments and 84% credit utilization.
Doesn't look like I was lucky enough for Fedloan to remove the lates for me, but they drop off anyway in December, so may try early removal in a few months.
TL;DR: It took less than a month for all the credit reporting to be updated on its own. My dispute did not really help at all in my case and I didn't bother to re-dispute.