Does there exist a mode of operation that forces mac-then-decrypt?
There is a type of AEAD construction, exemplified for example by the CAESAR candidate AEZ, which splits up into two components:


An enciphering scheme: "an object that is like a conventional blockcipher except that the plaintext’s length is arbitrary and variable, and, additionally, there’s a tweak" (p. 1).
An encode-then-encipher mode that enciphers the concatenation of a plaintext with a fixed number of zeroes (or some other alternatives).  On decryption, the authenticity check verifies that these final bits deciphered to zero.


The key thing is that in the enciphering scheme, a change to any bit of the ciphertext (or plaintext respectively) has a 50% chance of affecting every bit of the plaintext (or ciphertext respectively).  So attempts to modify a ciphertext will yield garbled plaintexts, and those garbled plaintexts will be safe to reveal.