That's going to be toward the bottom end of the range of drama-free cars, but not out of the picture. Are you flexible to go up to the $40-50K range? If so, your options will open up more broadly.
Folks here have tended to have the best success buying from fellow forum members, simply because the cars are much better known / documented, and there are throats to choke here vs. a HaT seller who is more often than not a flipper-dealer.
A good example of this is our member
@Jouser, who bought an extremely well cared-for and documented car from member
@TimL in the not-too-distant past. People here do regularly sell their cars, so it pays to be patient, and as you have, put the WANTED / ask out there. Patience is always rewarded, but it often takes time.
The more I see on HaT, the less enamored I am with the 500Es for sale there. Sure people document with tons of photos and such, but often the "overview" of the car's total care and ownership is scant and very formulaic. Compare that here to many owners, who create "OWNER" threads on their cars and/or ask questions and/or document maintenance jobs they do on their cars, with the guidance of folks here and the HOW-TOs we have. Much more valuable than an HaT listing.
So....keep looking, be patient, and thou shalt be rewarded !!