EDIT: I just read the part about 9 days... yeah, you are going to want to take it easy and keep your eye on it.
The rest I wrote before I read that:
The black tank has some margin for error in that it only backs up in one spot and it's pretty obvious.
Years ago I had the same concern so I decided starting with an empty tank that I would stand on the toilet pedal just to see how long it took to fill... I believe my rig had a 30gal black tank at the time... I quickly grew bored and realized that unless I was doing extended dry camping it was pretty much a non issue.
The gray tank is the one you will have to watch. I currently have a 10gal water heater and a nice large shower. When we come in from a cold day in the rain everyone like a nice warm shower. In an RV 10gal of hot water is a lot of hot water especially since it's being blended with cold.. after a day of showers, doing dishes and general useage I know I'm getting close to full. My current rig the gray will back up in the shower and while we have never had an overflow that is the one that I worry most about.
Enjoy..... I'd save the ice for mixed drinks and not worry too much about the sensors....
If you search there are lots of posts about different mixtures people claim will clean them... one involves Calgon bath beads, another is Fabric Softner, I've read about lemon juice and others... for me it was a fools errand.
I use a flashlight and look in the toilet and dump frequently.
2009 F350 CC LB 4WD
2017 Jayco 355MBQS