Sorry I'm late to the party. FWIW, I can get 300 fpm with a density altitude of 14000 feet in my Cessna 140. Also, FWIW I fly a 0-200 powered 140 with a climb prop and an empty weight of 990 lbs. As long as you're patient and can sacrifice a little bit of cruise speed, a 140 with a strong motor and climb prop will get you there. I'll have more info when I fly coast to coast in my 140 this October.

Singlespeed,
Did you ever find a plane? My flying has been on an extended hiatus for over a year and a half due to injuries. I have flown, but very little. I still try to keep up with anything aviation and might know of exactly what you are looking for. It's an O-290 powered Cessna 140. I had looked at it many years ago before I purchased a Champ (7AC-CONV with an O-235). The owner still has the Cessna and I can ask if he is still interested in selling. If you don't mind, let me know your budget and I can relay it the the owner. If it is within his selling price I can let you know. Send it to me via PM if you prefer.