Can I extend my stay in Thailand after my visa expires without incurring an overstay?

If your current stamp expires on the 6th and you go on that day to and see if they'll give you the 7 day get out of the country it sounds like you would still be one day short (as the 1st of the 7 days would be the 6th)

You can go to your immigration office and apply for a 7 day "get out of thailand" stamp that gives you a week to leave for 1900baht. Take proof you're leaving (some offices require it).

Also remember at most offices that 7 day stamp starts the day you apply for it (meaning it is not added to your current expiration date), so make sure when you apply when that 7 days starts

Best of luck with it, safe travels (y)