but it would be hard for the average tribe to butcher and consume and digest an entire big-game animal before the meat went bad.

I don't think that's correct. And they typically don't eat it all anyway. They hack off the fatty parts, eat some on site and carry a lot back. It isn't one person's family eating the bigger animal, it's shared out to the group on the understanding the favour is returned. Big game hunting is done in groups, not as an individual.

This leaving butchered large meat behaviour may well be behind the process of domestication in dogs, as we left a fair bit of meat to be scavenged.

It's also fairly common to dry meat for storage in HGs in summer, and in winter the cold extends usability.

I think you are overlooking the seasonality issue with food sources too. Get into winter and most of the smaller game will have hidden or flown away or will be so starved hunting it would provide fewer calories than you'd expend getting it. In temperate areas plant foods will be almost nil from late autumn onwards.

If this discussion is about the role of females in procuring hunted foods, there's one major issue that isn't being looked into. Personal safety.

Female HGs forage in groups, or they don't wander far from each other for a couple of good reasons.

First: Safety.

Bigger predators are more likely to take women and children than adult men. A female hunter is at a higher risk of death.

There's also the risk of your neighbouring HGs carrying you off or raping you, or both. A common occurrence in HG groups, where interpersonal violence is at a level much higher than we are used to. If female hunting was normal you'd have your neighbors lurking around the outskirts to trail them then take them.

This is the main reason female HGs forage in groups, or stay close to camp.

Second: assuming hunting is done with a bow, I doubt the smaller short bows females would have the strength to penetrate that deep into a larger animal. These wouldn't be like modern complex longbows. The force they produce on impact is lower.

Then there's the practicality of bow hunting in a group. A safe sized bunch of women stomping through the landscape are going to scare off most game. You'd probably have a decent chance at shooting something the others flushed out, but you won't be sneaking up on anything.

Then there's the mechanics of being pregnant, nursing or caring for a small child. IIRC female HGs tend to space pregnancies out every three years or so. This means for most of their adult life they'll be pregnant or breastfeeding a babe in arms. Not hunting during this time.