Here's a another feather for your cap. If it's overgrown more than what it would be for 2 weeks of growth, the first cut is even higher. When someone calls me weeks after the season started, I always ask when was the last time it was cut. Sometimes I'll charge double my mowing price for the first cut. I had a lady call and said her yard hadn't been mowed yet, but I was on week 7. Which means my EOW customers had already been done 3 times. So I figure how much they haven't paid for that yard yet on an EOW rate. I quoted her $200 for the first cut. She declined.
I also ask, do you want to get on a schedule or a one time cut. One time cuts get a little premium added too. I had a lady that her yard got away from her, and she couldn't get it cut with her push mower. So I did a one time cut to get it neat again. I told her as long as she runs the push mower once a week she'll never have issues. I also told her to call me in the winter to get her leaves up since there is a ton of leaves that fall in her yard.