I don’t know of any, but are you asking specifically to send in cartons to Amazon?
The reason why I ask is because you have one positive about the situation (like I do) in the sense that you live in the U.S.
So, if you NEED to, you can store like 500-1000 units at your home and ship them into an Amazon facility using the Amazon Partnered Carrier services which make the shipping really cheap. Usually a 20 pound box costs like $12 or something like that to ship half way across the country.
If this is something you can do, then it’s an option to send SOME of your order to yourself and just label the cartons when you are able to send them to Amazon (minimal effort on your part). Then you just take a few cartons at a time to UPS and ship them out.