Have you ever seen this unit working properly?

Do the connections on the input side match the incoming mains voltage?

Meanwhile, am I right in saying that the fuses that blow have been F5 (the 12V supply)?

(I'm trying to relate your symptoms to the circuit diagram I have here).

It looks like there are two solid-state relays in there; have you been able to confirm that they are working OK?

Any other clues? Like, does the compressor run continuously?

No error messages? think

If you don't inspect ... don't expect.