While we as professionals can't make any guarantee on the outcome, I would recommend writing the letter to clarify the situation!!! They can make exceptions and banks can write waivers for credit/income for USDA... So if they can make those exceptions, I think an explanation of the situation would be helpful. Certainly you did not intend to "cheat the IRS" and are showing good faith to correct the situation by amending your taxes. I've encountered several buyers in the same situation so don't feel alone! A knowledgable and motivated loan officer in this situation will be your best tool. It does make sense that you wouldn't have received 1099s because you weren't using a management company and most likely sounds like you own the property in your name.
I do recommend working with a CPA to find out the tax implications and make sure that they do not outweigh the benefit.... But going usda 100% financing will definitely be worth it! Excellent program for home buyers to purchase without downpayment. Good luck and I hope that this works out for you!!