On Time Delivery Rate (OTDR) - Buy Shipping Question

Hi All

I have found some threads relating to OTDR but can't seem to find a definitive answer to this question - If I buy all my labels via Amazon buy shipping does that offer any protection from OTDR?

I currently buy all my labels from Evri directly and ship everything next day. However, my OTDR tends to hover around 93% and Amazon then extend my delivery promise which has a huge impact on sales. For example, my offers are currently showing a delivery promise of Wednesday when in fact it should be tomorrow.

I don't see how I have any control at all for the performance of Evri, I hand all the orders over to them on time and that's all I can do. So I am wondering if change to Amazon buy shipping will it resolve this issue for me?