It looks alot like something I did for my last job. Comparing schedules to actual transit bus performance. It's really neat stuff when you start digging into distance/time. http://imgur.com/gmN3EfS
I was using PostGIS for vehicle tracking at my last job. PostGIS made it really simple by allowing me to boil everything down to simple geometry. The performance is amazing. The CTO told me I was doing it wrong and I should be using some homebrew solution in the middle tier that would do a comparison of 2,000+ points each GPS update. Why reinvent the wheel? Let the experts handle the geospatial functions.
I've been in this situation before. The my way or the highway attitude is a bad mindset to have when managing engineers. Skilled engineers are free thinkers and will push back on bad design. If someone says they can write something better than your spagetti code you shouldn't yell at them or make them feel inferior. You should allow them to build a system that will be clean and maintainable for the sake of all engineers that have to work on the codebase. Good leaders should know humility and when to admit they are wrong.
I had a similar situation happen to me, minus the going crazy part. If you constantly have to clean up because of the bad decisions of a manager then you should just leave that company. Don't bust your ass trying to make a difference and change minds that don't want to change. If you are an employee you are expendable.
I am not sure if the "just coast" advice would work. The source of stress is still there, still sapping away all the mental power, still occupying your brain during shower.
It all boils down to maintainability. Do I want to even attempt debugging or adding features to a 10,000 + line ASP.NET Web form page? What about a MVC project where someone took the time to observe separation of concerns and wrote unit tests for everything? Automated tests of any sort will save you when the code base grows, and it will. There are different code smells for different languages and platforms but the real developers will smell them out and see them for what they are, the wrong way to write software. Bad code is bad code and it is always the wrong way.
I do client side "MVC" with backbone every day. With proper architecture the possibilities are limitless and far beyond what one can do with a simple server side architecture. Using ASP.Net SignalR + Rest API I can have a fully reactive front end with little to no effort on my part. I work in the transportation industry and I can track a large number of buses and react to situations entirely with javascript being fed by a Redis Pub/Sub. I believe this is the direction the web is heading and one should not simply brush it off.
From someone that went from being in the military to software engineering I really believe this is a great mindset. We shouldn't feel like we are chained to one profession.