Private Student Loan late pays...Need help

[Emtmedic44]

I have two VERY old (from 2008) private/NOT federal student loans that were bought from a new servicer earlier this year. I thought they were setup on autopay but apparently they were not. I am currently showing two 120 day late pays on all three credit reports which of course has killed my credit scores and sent me over the edge into a deep depression. My husband was wanting to start looking at a new home and I have killed whatever chances we had of doing that anytime soon. 

My thoughts... the balances on both loans are low and can be easily paid off. $1400 total 

What are my chances on calling the servicer and offering to pay in full if they will delete any or all of the reporting late pays from Oct, Nov, and December? I haven't missed a payment in the past two years. If they decline with the usual we have to report the truth blah blah blah.. pay them off and start sending off disputes with the hopes that at some point since they are paid in full the creditor just won't respond and the entire tradeline will be deleted? Any thoughts or advice would be greatly appreciated!