DES-CBC with random IV - how big is the keyspace? Can COTS tools crack it?
Is the keyspace really 120 bits?


No. It's still 56 bits, at least when multiple blocks are encrypted. For CBC mode then you can try and decrypt a block with the key, XOR it with the previous ciphertext block you should get a plaintext block. If you did this for the last plaintext block you'll have the PKCS#5 padding to find. If that's correct then you can start looking if you can produce valid plaintext.

If only one block is encrypted then the IV acts as a one-time-pad. In that case you will have to guess the password (presuming you have the salt of course).


  Am I missing something or is hashcat not capable of cracking this? 


Could be. But it would probably not be that hard for an accomplished programmer to program it in. Hashcat seems to focus on the password hash itself. Assuming the password is not too complex, guessing it may still be the best way to try and decrypt the ciphertext.


  Can other tools crack it?


Well, cracking single DES can be done by specialized hardware for sure (a list is here). Asking for resources like that is off-topic though.


  Is it even possible to deduce correct outputs without making assumptions on expected output (eg all output must be ASCII data, or match a file header)


Well, other than the padding, yes, you must be able to test if the plaintext is comprehensible in some kind of way. However, if you decrypt many blocks the plaintext is likely not all that random, so you could test for that. If it compresses well, for instance, it may be worth another look (but compression is generally pretty expensive).