I like where you are going with this. Here's my suggestions.
1. For spells known, to me, the problem is at higher levels. Adding +Cha to spells known seems like it overpowers the class at 1st level, making it even more attractive for a multiclass splash. Instead, I'd just give the sorc 1 new spell at every single level, instead of going to every-other-level after 10th. I could see an argument for giving them +1 spell at 1st level, too, so that their spell chart goes from 3 spells at 1st to 22 spells at 20th. That's still the fewest spells known/prepped of any full-caster, but at least it's in the same ballpark.
2. For sorcery points, I favor a varaint of option C. I don't think it fails criteria 3 at all; quite the opposite. And I don't think you need to fail it on criteria 1, either, since it's much easier to explain than Arcane Recovery or Natural Recovery. Here's my proposal: "You regain all spent sorcery points when you finish a long rest, and half your spent sorcery points when you finish a short rest." Note that it's half your spent points, so you recover more if you've spent more -- encouraging players to use 'em or lose 'em. A character who burns through all their points all the time and gets multiple short rests in may come out ahead of a wizard or druid's recovery in terms of spell slots regained, but this seems like an edge case. I really like the flavor of this proposal: the sorcerer is resting, so they get back some spent points, makes sense to me.
However, I'm still not convinced that the number of sorcery points is the problem. To me, the worse problem is the selection of metamagic; some of the metamagics are way better than others. For starters, the weaker options -- Distant, Extended, Subtle -- should just be given to all sorcerers, for free. I'm not sure what else could be done here. I'd almost be OK with giving all sorcerers all the listed metamagics for free, and let them use their metamagic picks to learn more exotic tricks (like energy substitution, delayed-trigger spells, spontaneous casting of spells they don't know, etc. -- I might make Twinned one of the exotic metamagics, too). That's a much heavier-weight change; more of an Unearthed Arcana class rewrite, than something you can punch in as a house rule.
A single new metamagic may address both problems:
Spontaneous Casting. You may expend a spell slot to cast any spell from the sorcerer list of the slot's spell level or lower, even if it's not one of your spells known. This costs 1 sorcery point per level of the spell slot you are expending.
That would allow people who are dissatisfied with the sorcerer's limited number of known spells to burn sorcery points to whip out some really flexible spellcasting, without impacting the balance of the game much at all.