In my thinking, mailing your renewal a week early should have been sufficient. In Texas, they go by the postmark. I sent mine "RRR" to prove I mailed it on time. It took about ten days, but finally my education credits were updated on the real estate commission site, my check was cashed, and my license renewal was sent to my broker. Guess what--when the receipt came back, I found that the post office had delivered it to the wrong state commission and someone there had signed for it. I was so fortunate that whoever ended up with it figured out it was important and forwarded it on to the real estate commission. I had written "license renewal" on the front of the envelope, so that was probably why it made it's way to the right place.
In your case, if you continue to practice real estate and your real estate commission never gets your check because it got lost at the post office or in their own office, they may conclude that you did not mail it, and therefore that you are in violation of your state's real estate licensing act, acting as a real estate agent when you are no longer licensed to do so. I assume that is what you are worried about.
It shouldn't take 4-6 weeks for them to update their records. That may be a worst case situation. I wish I could suggest something other than just calling them every day. If it doesn't show up soon, ask your commission if you can mail another form with another check in overnight mail. Of course, you will be filing late if they have to use the second check, so there may be some kind of late fee.
Each state if different and I'm just guessing at all this, so let your real estate commission be the last word. I'm sorry you are having this difficulty. You mailed yours a week early and are having problems, but I mailed mine on the expiration date, due mainly to my being down to the wire taking my required (math) test, and had none. In this case, life does not appear to be fair.
Darlene