Have not played it, but there is this...
Blood & Bronze
I think at one point they had a freebie preview- I can't seem to locate my copy though (different computer). I believe it is D6 dice pool based.
I think that with some tinkering to make it more heroic- Various versions of RQ work well-especially Openquest-which diverges a bit from the deadlier combat system of RQ by ignoring the Hit locations (and thus lots of lopped off limbs, etc). MRQII as well.
Exemplars and Eidolons
Drive Thru Link is a OSR retro style game that is worth checking out. You are very much a Demi-God type character ala many Bronze Age mythological heroes (it's free, and I've had a blast running it- def worth checking out). TSR D&D compatible. Your PC's do HIT DICE of damage, instead of Hit Points in combat
Arrows of Indra is a game I believe that is set in a Fantasy/Mythological version of India
That said-
For me Bronze age is more about the Setting, and not necc the rules. Empire of the Petal Throne gives me the Bronze Age vibe, yet it's ultimately Science Fantasy with underground dungeons (tunnels for ancient train systems) and "eyes" (ancient advanced tech). But the cultures are very Bronze Age in feel at this point in their evolution. There's plenty of versions of the game out there-I believe The Tekumel Hack is free.
There are elements of Exalted (1st Edition) that also give me that vibe. Though clearly it went full on Anime/Wuxia in a short period of time after introduction.
Bronze Age would probably need to be re-worked to make it "sanitary" for the modern RPG market. Things that are very common during this time- Sacrifice, Slavery, etc would be a problem for some.
Some things that are absolutely necessary, IMO-
1) Mythology is "real"- Magic and the Gods do not have to be as prevalent as Glorantha, but the Mythology is real, and the heroes can interact with the gods in some manner.
2)There is no pseudo science Magic Guilds or such, but spirit magic. divine magic. perhaps, elemental magic. Magic items would be cultural artifacts made by the Gods- The Golden Fleece, Perseus' Shield, etc. Most magic is probably seen as evil/demonic.
3) It should go without saying, but the technology level should be appropriate. Anything more advanced (or even things just rare to the vast majority) would be "the work of the gods" or "demons", etc,
4) Humano-centric- this is just personal pref. As amazingly crafted as both worlds are, I don't really care for the alien races of Tekumel, or Elves/Dwarves/Ducks/DragonNewts etc in Glorantha either- despite being a long-time fan. These are elements that always break immersion for me and put me into "High Fantasy" state of mind.
IDK, just my initial thoughts.