I had a similar problem at my wash. I used one of these, to give the problem area a reserve of water at the pressure I needed. Worked great.
http://www.harborfreight.com/1-horsepower-shallow-well-pump-with-stainless-steel-housing-68387.html
Bubbles-John,
I would go for all the rest of the solutions suggested first. When I corrected our low pressure with the larger piping at the pertinent point we also helped the overall situation for other needed fills around our facility. In other words ---- especially if the pressure loss is a factor for the Automatic somehow.
When Washmee-Jon says he has first hand experience with the stainless pump-tank -- it sounds like it could be an option --- much better than your Menards choice. Take heed to the review that says a check valve is a must if you use it. The 50 PSI seems to be on the border of what you need for the Pet Wash Watts Regulator valve --- I am not sure.
Washmee-Jon
I notice on the specs ----- "6.3 gallon hardened steel alloy tank"
That sounds like it is not all stainless steel --- I wonder if your application is less sensitive to small amounts of rusty water than what a Pet Wash would want to allow.
mike walsh king koin of bismarck