How did you avoid 'late shipments'?

[cedarstone_industry]

So, we use USPS. The majority of shipments are under 2LBS, which leaves USPS the cheaper choice against UPS and Fedex. Customers will 90% of the time only pay for First Class. Items that are 1LB or more, however, have to be shipped Priority with USPS. So very often we will out-of-pocket pay for the shipping difference as a kindness to customers for the time being. (At some point I will bake shipping by weight of item into its price.)

Yet we are facing an onslaught of late shipment defects. The first issue I notice is this: Say I have an order on the 17th. I pull it, pack it, and create/print the label on the 17th. It is then handed over to USPS. When I go to check tracking I will see 'Pre-Shipment Info Sent to USPS, USPS Awaiting Item'. But the date will ALWAYS be 24 hours later. It will claim this on the 18th, not the 17th. And a good 50% of our packages will then not be scanned at our USPS location EVEN THOUGH a scan sheet is being given with my shipments. 

Most days now our postman picks-up from our location. We have schedule pick-up every Mon-Fri for the rest of this year. If he does not show before we close, a lead employee will drop our packages off. He also has the scan sheet in hand. (The paid scheduled pick-up is too costly for us at $22/day.) Everything is same day unless an order is placed after 4 PM, let alone on Friday. In these cases, I will get to the order Monday morning following. (This should be within the 48 hour handle time due to business days.)

With all these no scans, how do I prove an item as handed off to USPS same day as label creation? Mind you, when it is a postman pick-up in most cases. With the routes as heavy as there are I can't possibly have this poor man stop and set up some sort of documentation can I?

Besides that, USPS estimates their delivery of course. If eBay has a different estimate than USPS what can I even do? If eBay says the 21st but my tracking shows USPS assume 23rd . . . and then the item gets there by the 23rd . . . Why should eBay strike me for their estimation? Why is theirs above USPS's own?

I have reported this USPS location to HQ. This is after I tried speaking to employees there. All of which were very polite but, the issue was not handled obviously. I then escalated the issue when no changes seemed to be happening. There is no closer USPS, or even within a range that the extra drive would be acceptable for dropping off ourselves. 

So what do I do at this point? I handle orders in 24 hours. I know for a fact I have the packages out to USPS same day. I have created scan sheets and handed them off. What more can I do?

These late shipments are dropping us under standard here on eBay.