So this is the post that is closest to what I am trying to get at.
First, I truly appreciate the many great comments and ideas that people have already come up with. That said, addressing a few that are helpful to others, but not to me:
A. Yes, while I am a maniacal and tyrannical despot who lives to ruin the fun of other people, this is driven by player demand as well. Without addressing this issue, I have a feeling that my "core" group will be returning to 1e or B/X in the future, and I'd like to stick with 5e.
B. Titles need to be pithy; that said, this isn't about having a "low magic" game. If the table just wanted low magic, there are very easy (if unsatisfying) fixes- like the party of 6 champions.
This is about removing cantrips (at will magic) and fixing the spell-equivalency system. In short, this post comes closest to what I've been thinking:
1. Remove cantrips.
2. Fighters, Monks, Barbarians, Rogues are restricted to non-spellcasting subclasses. Any incidental uses of spells or cantrips are removed or re-written as class abilities.
3. Wizards, Clerics, Druids remain relatively unchanged (other than loss of cantrips).
4. Sorcerer (to a lesser extent) and Warlock (to a greater extent) ... I don't know. Not sure how easy that they would be.
5. Paladins, Bards, and Rangers re-done to remove casting. For obvious reasons, as you point out, bard would be tough. And Paladins could just be removed.
I'm thinking this would be a good start.