Everyone has varying definitions of Midcore Content and what it needs to have a longer shelf life.
Would you classify Eureka/Bozja/etc. as Midcore? I suppose you could. BA, Delubrum Reginae, etc could all technically count but these are instances within instances that require a grind just to unlock. The problem comes from the fact that these are kind of time sensitive grinds. If you aren't there when the content is relevant, you'll have a hell of a hard time actually doing any of that content with any frequency.
Variant/Criterion Dungeons should've been the answer since they essentially let you skip the prerequisite grind in order to unlock the content but due to a lackluster reward system and that the content is objectively difficult for the sake of being difficult, it fell off quickly since there wasn't really any reason to go along with it outside of whatever rewards you were trying to unlock. Sure, it appealed to those that like challenging content but since Savage already grants you difficult content and with tangible rewards to go alongside the work, it becomes less appealing. Since they're going to take another stab at Variant/Criterion Dungeons, all they would have to do is make gear that is equivalent to Unaugmented Gear but with a 3rd Guaranteed Materia Slot and the content becomes at least relevant. It wouldn't invalidate Crafted Gear for Raids since you can overmeld that, Unaugmented Gear has the benefit of being upgraded but for those people that want to engage with this type of content, there's a fairly nice carrot on a stick for them. If they don't want people to just grind for a full set of this gear, just do what they always do and put a limitation on the gear, be it weekly lockout, currency grinding, etc.

Now I'll be the 1st to admit that this is a shortsighted fix but the fact is that people like to see themselves progress. Be it level, gear, some collectables that they enjoy (Mounts, Minions, TT Cards, etc.) getting SOMETHING worthwhile does help to keep content relevant for longer than if it wasn't the case, hence the current state of V&C Dungeons. It's a bandaid fix instead of a full on solution but regrettably, solutions that don't require waiting until 7.0 aren't exactly going to happen either. Salvaging it for now would be for the best until a more permanent solution can be made.