Sounds like you need to find a guy, kid, whatever that enjoys watching you race. You pay his way into the track and have him change your tires. Except saying you don't have time to change tires, I see nothing that doesn't line up with what I recommended. It's like you said all in one sentence that you are getting serious about racing but don't want to go fast...
You run a tire that works well for you on the street on rims that you like the look of. At the track you bring an aluminum racing jack and cordless impact gun and take 10 minutes to swap to rims and tires that do far better than your street tires on heavy rims ever could. Every track I've been to opens the gates before the lanes so I don't know how you can't have time to change them. Again I'm not saying you need to run a $2400 set of cheater slicks on custom rims; PYOs with some relatively soft street or AT tires have done me very well in the past, cutting consistent 1.6s and running much faster times and traps than I ever could on my 20s. Additionally you don't tear up your DD tires. It's like not wanting to take 30 seconds to pull the tail gate or 3 minutes to pull the passenger and rear seat then complaining that a guy that does beat you because he "stripped his truck". That's not cheating, it's prep for racing. It's cool to say "I ran 12.9s exactly how I drive it every day" (except that you were on a prepped race track with a tree and trap lights); but I'd rather say "I ran 12.5s."