I'm not sure how "minimal" you'd consider this one, but I've implemented the following in my very Sword & Sorcery inspired 5e campaigns (which are really a mishmash of Primeval Thule, Xoth, and Astonishing Swordsmen and Sorcerers of Hyperboria):Yeah well, that's not what I'm saying.
I'm saying 5th Edition can be a good choice for S&S. In many areas it is actually the best edition for S&S! It's just that you need to sacrifice the convenience of the regular spell framework. Actually I think you need to make far less intrusive changes than you might think. You do need to go further than just "no fireballs" though.
Instead of simply telling fans of the genre "this is as good as it gets, if you want more use a different system", I would be interested to discuss how to minimally tweak the D&D spell-casting rules to (much) better support S&S tropes (for player characters).
1. No damage-dealing cantrips
1a. No spellcasters except warlocks
1b. Magic Initiate feat is OK, but see 1, above
2. Use the patron-specific Warlock class features from the Primeval Thule Player's Companion
3. Limit healing potions to Keoghtom's Ointment (renamed in my campaign as Nergal's Blessing
4. Spellcasters are feared and despised by everyone.
5. There is exactly one of most magic items, especially magic weapons. So you don't go seeking A flame tongue, you go seeking THE Flame Tongue. And you can be sure that others are seeking it too.
I ran a bunch of 5e campaigns using these guidelines, and it's worked pretty well.