And from this DM's perspective what you want sounds heavy, slow, and clunky. And much clunkier than Daggerheart is.
"A few books". With the sole exception of a couple of monster statblocks and a map if I need books in play and this isn't my first time running it then something has gone badly wrong or the game is too clunky. Daggerheart, incidentally, passes the test. And although Daggerheart has a DM screen again that's weight and a barrier I don't need.
Instead all I need for Daggerheart are a tablet for bookmarked stat blocks and notes, and some dice - although I also like tokens for fear (I could just use a D12 and no monster in the game has more than 12hp so I use dice for monster hp and stress).
The players have their character sheet (single sided in play with the other side having background info and instructions on levelling up), between 6 and 12 active cards depending on level, dice, tokens (dice can be used), and a pencil each.
So what on earth do you run? Fate? Risus? Actually it can't be either as they aren't so clunky and slow as to need the books in play.
You must despise every edition of D&D with the passion of a thousand burning suns. The standard you have set literally does not allow a character to read a spell printed on their own character sheet with the full text of the spell sitting there in front of them; it's almost always faster to find the card with the bright evocative artwork for the spell or ability in question sitting face up on the table than to flip pages and scan down to find the dry text of the spell.
As for the cards? They contain all the other character rules anyone needs already printed out. There is zero time spent being unable to read handwriting. Zero time spent flip flipping through pages of a large, heavy, and clunky rulebook to find the spell, feat, or class feature. Instead the player always has it to hand unless they have somehow lost it since the start of the session (which hasn't happened yet). And the spell or ability is written clearly and succinctly.
Based on your stated preferences you must either run something ultra rules light that somehow requires multiple rullebooks and a screen? I'm curious what it is?
Either that or you have dismissed Daggerheart without having played it despite it being actively superior at what you claim to value to any other game remotely of its complexity. (Does this make it the best at everything? No. But the cards really do help keep the pace from slowing for the rules).
