I like cassette decks but I don't trust auto-reverse mechanisms. Especially if they're cheap. Tape playback quality ( and recording but that's another issue ) depends so much on proper physical alignment of the tape with the heads that it seems nuts to build in a gadget that will invariably tend to throw the alignment out.
That said, I would consider a Nak 202 or 505, or that Uher portable which was not much bigger than a paperback--such elegance. But they're not low $. So sorry, this is not an answer to your question, it's a suggestion that your question may be an oxymoron like "jumbo shrimp".
That said, I would consider a Nak 202 or 505, or that Uher portable which was not much bigger than a paperback--such elegance. But they're not low $. So sorry, this is not an answer to your question, it's a suggestion that your question may be an oxymoron like "jumbo shrimp".