Is this EAX extension weakening the (provable) security of EAX? I would like to insert a key deriving function into EAX mode, in order to hamper brute-force attacks for a key-size restricted cipher (56 bits). The modification inserts an identical multi-block pattern $S$ behind the corresponding tweaks:

Original: $OMAC(T||...)$ where the 128-bit tweak $T$ is either 0, 1, 2.

Modification: $OMAC(T||S||...)$

The state of the MAC behind $S$ is different for disjunct tweaks, because the MAC's state behind $S$ can be decrypted back to the original tweak, and identical states would yield identical tweaks.

Is this EAX extension weakening the (provable) security of EAX?
So you want to use EAX with a block cipher with a 56-bit key. Presumably, this is for a good reason.

Your idea is to include a (long!) fixed string in the OMAC to slow down nonce creation. Since the attacker must know the nonce to test if a key is correct, this should also slow down a brute force attack.

Instead of modifying EAX, you could use EAX in a slightly different way: Always prefix the EAX nonce by S, and always prefix the associated data by S. This seems to be equivalent in operation to your proposed modification. I don't think the EAX security proof covers this specific case, but I wouldn't be surprised if it could be adapted to this case. (Probably, you could argue that a random-looking function remains random-looking even when its inputs are restricted.) Which means that this should be ok.

You should note that including S in the associated data doesn't hinder the attacker, only the users of the system. So probably, S should only be included with the EAX nonce.

PS. You need a really good reason to use a 56-bit block cipher today.