Just a thought, but perhaps the Klamath Co. Library (on Klamath Ave. in Klamath Falls)might have a city directory for Klamath Falls during the 1930's?
If you come here do try to take the Trolly ride around town. It only costs a couple of bucks (or maybe even one, not sure)and it gives lots of info. of the towns history. If time allows the Baldwin Hotel is a great place to visit for those who like to step back in time.
For eating places that are really good: Antonio's, Italian food, on Main St.. Sergio's, mexican food, on So. 6th St.. Sam's Restaurant, good american food, on Washburn Way (Washburn Way intersects with So. 6th.) Klamath Falls is a small town and just about anyone can direct you to any place you want to go. :o)
I hope a trip to Klamath Falls for anyone is an enjoyable one. People are friendly and helpful here.
May I ask where you would be coming from? If that is too forward please forgive me.