Love a good business problem and your methodical approach however I wonder how you came up with the $3/cost/wash? At 39 cars per day and $3 cost you are saying that total variable costs per year will be $42K or $3.5K per month which seems a bit low for a big city location. A plumber can cost $500/visit without much being done.
You probably will want someone (even part-time) to help to keep the place clean and running smoothly unless you plan to be there 100% of the time. When I did my analysis for a recent purchase I broke out my fixed and variable costs so I know the nut I need to cover each month (loan cost, property taxes, basic electricity and water with little use, insurance, security cameras & monitoring, promotion, misc) in the event that I get zero business (due to weather, equipment failure, snow, or some other unforeseen issue), then you understand the true risk and know if it is acceptable. Plan for a 10% variance in building costs for unforeseen expenses and have enough funds to cover you for 3 months of fixed costs if the project timeline slips or it takes time for customers to notice you.
Add some money for promotion and advertising as you are a new location and want to get your name out there.
You probably want to double check the water, electric, and sewer rates to make certain you are on solid ground as they often can vary significantly by county in some states as those costs explain the difference in profitability and survival. Huge difference between counties in Maryland.
Your construction numbers above are consistent with the ones I received when I spoke with WW, New Horizons, a sign company for a LED sign, and other similar contractors. An ICS Paystation that will allow you to market and upsell your 3-4 wash packages not to mention have a monthly (RFID) subscription plan will cost you $50K (for each bay). Monthly plans seem to be the way to go to
lock in some consistent revenue flow. What about floor and bay heating? Are those costs in your numbers as I know radiant heating in cement can be pricey. If you live in Chicago I have to think that it is a must have item given the weather otherwise you are fighting the freezing water on the ground all the time for several months.
I purchased a 30 year old 6 bay car wash that was in need of an overhaul and in the process of adding a WW Touch-free machine and probably updating the other equipment in the SS bays - it's a project.
Lastly, nice to be your own boss so go for it as it sounds like you are taking the right approach to the business challenge.