What do you mean Day 6 is too early? Too early for what?
I've hatched two different shipments of eggs from the same supplier in two different years. Both were packaged the same. One hatch was a 20% success, the other a 100% success. The oldest of the shipped eggs were about 5 or 6 days old when they were shipped and arrived a couple of days later. They were shipped by truck not airplane.
Before he retired my brother was a rural mail carrier with the post office. He said most Post Office people handled fragile packages with care but occasionally one specific employee would toss them around. Don't assume all Post Office employees are lowlifes with no moral upbringing. It is like in any other profession, you get all kinds. Most are decent people.
Some shippers are not going to handle them wisely before shipping or may not package them well. Many will. Some shipping will be handled well, some will not be. I do not know how to control either the shippers or the shipping. To me it is blind luck.
I don't have any solution to the problem if you want specific eggs from a distant source.