For the 5 algorithms you mentioned, I know them well.
> SHA-1 and AES also vary by the round
Vary what by the round? SHA-1 ( https://www.nayuki.io/res/cryptographic-primitives-in-plain-... ) is structured very similarly to MD5, with one big difference being that SHA-1 doesn't vary the rotation by the round number. AES has a public sequence of round constants that gets applied to the key expansion, but otherwise doesn't do anything special to the ciphertext per round.
The logic that can cause timing issues include using a memory lookup table for the S-box and finite field multiplication in AES, as well data-dependent rotations in rare ciphers like https://en.wikipedia.org/wiki/RC5 and RC6.