OP, your statement about keep the mower up high to achieve the best grass. That's what I tell my wife when she says the grass is getting tall. I tell her I'm keeping it healthy.
Serously, no pics, but we recently moved to a new house. We have zero trees in the front yard, which means I'm taking over nice grass. First thing I did was spray out the weeds I found. I plan to keep it nice where before I had the same philosophy of another Pinsider; if it's green it's good.
I'm also guilty of not changing the oil in a mower for 10 yrs. The thing ran great and the first oil change I did was when I sold it because my FIL gave me a better mower.
I put up with two Sweet Gum trees the past 14 years and regret not cutting them down on year one. They were a constant problem. No Sweet Gum trees for me now.