And in the vein of talking about tone and genre... Exactly what do we think? I mean, "Mythic Heroes" are an oddball category! First of all VERY few of them are actually human in the myths of this world. 99% of them are demigods or something like that, if not outright gods. It does shade a bit into "super powered humans who were fated to be extraordinary by nature" here and there, but basically the D&D 'adventurer model' isn't all that consonant with mythic characters.
OTOH, I've kind of wedded myself to the core D&D-esque model of a power progression over time for PCs, and that also is a bit off from myths to an extent. I mean, most mythic heroes seem to have innate talent, or talent that was developed offscreen and generally started with some kind of supernatural origin. Now, you could build on that and say that every PC in HOML is a 'nascent hero' and has the potential to be mythic, and they are all supernatural in origin. I'm not sure how to convey that. I mean, I could lean into it and make 'supernatural origin' a big part of a PC build.
OTOH LEGENDS are much more amenable to being portrayed in a classically D&D-esque way. Beowulf didn't start out as a super bad-ass, he was perhaps talented and maybe fated, but at some point in his youth he was just a fairly ordinary warrior of unusual talent. Heck, even at the end he's not a MYTH, he's just an exemplary human, the dragon still beats him!
I guess the question is, are we dealing with outright MYTHS, or something closer to LEGENDS? The later fits a lot more easily into a paradigm similar to D&D, which works well for a 4e-like game. It is certainly possible to go further and stick to the 4e paradigm of Epic play where you BECOME a mythic figure, transcending legends. The difference being you're not really addressing classical (say classical Greek) myths exactly. It is maybe closer to the RQ "hero questing" kind of design where you get to Mythic Tier and then you start running into gods, adventuring in 'heaven' or 'hell', etc. Again, we just go along with the 4e model here, pretty much.
I'm really not sure how you would even approach the classic myth sort of model. I guess it would be a bit like Exalted or something like that where the PCs were created de novo as supernatural beings of some sort and that was that. It sounds like an interesting concept, but I'm inclined to stick with the "you are a hero from the start, but not even a legend yet, and entering into Myth is something that some mortals do in this world" Maybe when you reach Mythic Tier one of the boons you can get is a revelation of a supernatural element to your nature that manifests at that time, sort of like an ED.