Parallel file encryption and authentication for large files
To answer your ideas of:


"I use hash-then-encrypt" with CBC + SHA-1
"I use MAC-then-encrypt" with CBC + HMAC
"I won't use GCM because of unclear usage guidance"


First, hash-then-encrypt is a really bad idea. You really should avoid it if possible. Details are explained in this related question on Crypto.SE.

Second, MAC-then-encrypt is a concept you also should avoid. Not only do generic compositional security proofs don't generally hold, but it also allows for padding oracle attacks in some circumstances, so encrypt-then-MAC is better and there's no significant advantage to use authenticate-then-encrypt over the more generically secue encrypt-then-authenticate. Also see our canonical question on this subject.

Third : GCM. You indeed only should encrypt than less than 60GiB of data under a given key-nonce pair. However, you could assign (ascending) nonces to your data chunks (of a few kBs each) and authenticated encrypt them each using a different nonce. This way you stay way below the 60GB limit and you generate your nonces deterministically (using counter incrementation) which will also quite reliably protect you against nonce re-use based on nonce collisions. Upon retrieval of the data you could just check then whether all chunks are valid and whether a chunk is missing (because there's a gap in the nonces) and maybe you'd want to encode the number of chunks into each chunk to allow proper verification.