I was traveling around on my own in a 30' Bounder 30E motorhome. It has a 100 gallon fresh water tank, 59 black, and 42 grey.
I would take daily showers, and the 100 gallons would last me about 2 weeks. If I wanted to stay 3 weeks+ I could take along some 7 gallon blue fresh water tanks, and fill them while out sightseeing.
You can conserve water by using a dishpan. If in the shower, you can collect some of the water and use it to fill a gallon container, to use to flush at night, saving grey tank space and fresh water. When doing dishes, you can also do them in a dishpan, saving the water to flush, or toss it on the thirsty grass to save space in the grey tank.
Of course if you are camping on private property, or very diversed camping you can sometimes dig a 12" deep hole, drain the grey tank, and bury the hole (to prevent flies from gathering) and prolong your stay until the black tank is full.
I would fill my 18 gallon propane tank every 6 weeks while full timing. Your 4.5 gallon tanks would last about 2 weeks - if you are not using the furnace much. It is fairly easy to refill on tank at a time while out sightseeing or driving from one location to another.
Have fun on your travels.
I have a 400 watt solar system, so I rarely needed to run the generator, the solar would make up most of my power use.
Once every 2-3 weeks I would go to a local town laundry mat. I would take over 3-4 of the large tumbling washers, and 4-5 of the dryers. This way I could do all the laundry in only about 3 hours from the time I was loading my car until I was hanging it all up back at the RV. This is much less time that I would spend in 3 weeks laundry at home, one smaller load at a time.\
Have fun!
Fred.