Run water from your fresh water tank and use the on-board pump. No worries about anything that way. No worries about over pressure, or pressure regulators, or check valve failures, or back filling and over flowing into the fresh water tank, or hoses laying in the grass for someone to trip over, or hoses on the ground that could potentially burst.
The trade-off is: You do have to fill the fresh tank and keep an eye on usage (which makes you conscious of your water usage and I think makes you a better more responsible citizen). You do have to be aware of the cleanliness of your water tank. And you will get some noise from the water pump when it runs. But, you do not have to worry about anything pointed out above, which is exactly why we run water from the tank and use the pump all the time and never connect directly to the city water connection.
I suggest you run water from your tank using the on-board pump for a while and see if that cleans out any particles that might be affecting the check valve or back-flow valve, or any particles caught in the pump itself allowing a back flow situation.
