Is XTS basically the cheapest form of (secure) double-encryption?
So is there any way to break XTS or a double application thereof in less time and/or space than expected?
The expected time for standard XTS is time $2^{512}$ for 256-bit AES and $2^{513}$ time and $2^{512}$ space for double encryption.

Yes, there are better attacks than that.
With XTS a single sector is encrypted with a single $E_{K_2}(n)$ value, so the attacker can treat it as constant. It is only 128 bits, so a brute force attack can find both it and the AES key $K_1$ in about $2^{384}$ time. Once the attacker knows $K_1$, they can separately, given multiple sectors, attack the key $K_2$ in negligible time compared to the first step.
A meet-in-the-middle attack applies on double XTS as normal, in about $2^{385}$ time and $2^{384}$ space.
Note that with AES-128 the above would not be the case, since $K_1$ is the same size as the block, so a brute force takes $2^{256}$ time regardless of whether you are looking for the key or the encryption of the sector index.
There are of course other weaknesses that have to do with the fact that it is deterministic and lacks authentication. You can look at it as a sector sized cipher in ECB mode, if the attacker can see multiple ciphertexts for the same sectors. Any random string is a valid ciphertext, due to the absence of authentication or even padding.
XTS should not be used as general purpose encryption when IVs and authentication can be used.