Your point about shipping overnight on the weekend cannot be ignored. While it is available through the USPS's Priority Express (which includes Sundays and holidays), from what I can find, that is only available in larger metropolitan areas.
Riley says the letter appears to have been written after GP died, and he states he was led to believe BL got the letter before he arrived back in North Port. These are not definitive facts, of course, but if this is what they believe, then the letter had to be sent to somewhere for BL to receive it, it had to have been mailed and picked up between Aug. 28 and Sept. 1, and no matter how much it doesn't make sense, it had to happen (if their timeline is correct).
If BL killed GP on the 27th, he chose to hang around the area for at least two more days. Why? It sounds good that he was waiting for a package delivered to Jackson, but maybe he wasn't. Maybe the package was going to be mailed to another location along his route home and he was waiting to time his arrival on the right day. He could have picked up the letter at any point, including as late as Sept 1. Maybe the letter was never even mailed, but left at some location in FL, where he could pick it up before he got home. Maybe this was all an attempt to communicate without being traced. IDK. It sounds ridiculous, but the dates are what Riley provided, not ones we are making up.
So much of this lawsuit goes against the direction I have tended to lean towards in regards to the Ls knowledge, but as has been pointed out, what the lawyers are saying, and the claims being made, have yet to be substantiated publicly with evidence. However, that doesn't mean the evidence isn't there, we just don't know.