MMEL shouldn't be applicable under 121, where the MEL is issued to a specific aircraft, and may or may not be set up like the MMEL. The MMEL is the master list, and the actual MEL in use by the fleet or the individual aircraft doesn't necessarily correspond with what's listed in the MMEL.
You're not implying that both ILS receivers are inoperative if you release based on something else; they're only inoperative if they're MEL'd inoperative and are identified and placarded inoperative.
You can't simply get FSDO approval for an alteration to the MEL; it's got to be done specifically through your POI in relation to company operations, in accordance with your OpSpecs section D. That is to say, it isn't simply an appeal to the FSDO, but must work within your company relationship to the FAA, and must pass through maintenance and operations.
It sounds like you may be talking about ILS antenna switching logic, from upper to lower antennas for the approach? If that's the case, you may not need to MEL the equipment inoperative; if one of the two locations is inoperative, or the switching is inoperative, it may simply be an (o) procedure allowing the use of a minimums additive to achieve the same level of safety. You'd have to refer to the aircraft limits as well as the MEL.
If you're looking at the MMEL for a fleet MEL change, that's another matter. I'm unclear on your view here, whether you're looking at it as a dispatcher, or as maintenance, or as a pilot, but the ultimate end seems to be the same: can we do it, or can we not? If that's the case, I don't see any reason why you can't operate without the ILS under 121, but you'll still need adequate equipment appropriate to the facilities, unless you have some company guidance restricting you, and won't need the ILS at alternates or diversion fields.