Alot of my customers offered water from their outside tap to begin with. But most have no idea of the filtration process of ro.
They think that it will be a couple of litres and most will be appauled at the waste water going down the drain, especially if they were on a meter as well. I would see myself paying for the water to clean all the neighbours. So when I found out the implication of my offer for water, I would cancel your services.
In the winter time I have found that most people switch their outside tap off, so that won't help you either.
To run an r/o efficiently, it needs long running times. Stop start isn't good.
I have 650 litres on board and the only time I use all of that is when I have the flow rate up too high - yes rinsing is quicker, that I find that I waste more in the scrubbing phase of the clean with a high water flow.
The suggestions to turn the water flow down are valid in my experience. I also use an Aquadapter.
If you are hell bent on filling up along the way, I would consider a double tank system ie 2 x 350 litres. Fill both tanks with pure to start the day, empty the first and then switch over to the second. Use a outside water source/sources to fill the first tank with tap water. Move off to another house and use a shurflo 12 v pump to filter that water through a 4040 r/o. You can position your van over a drain grill in the road so the waste water doesn't create too much attention. You will be processing that water into the second tank you are using. Hopefully you should get around 175litres of pure out of the 350 litres of tap water.