From the comments by Don.
My point is that even under the best conditions, the caloric delivery of hunting ebbs and flows, whereas that of gathering (including collecting small game) remains fairly constant.
Under such circumstances, an omnivorous species would naturally adopt gathered plant foods and small game as its basic diet, while also making an effort every day to obtain the prized large game, sometimes succeeding and sometimes not.
Some words of wisdom.
Basically we would have adapted to the diet that we had, rather than the diet we would have liked to have.
So Tubers and Nuts would have been a major part of our diets along with meat. Berries, and vegetables would be a smaller (caloric value) but a regular part.
I am not sure if Nuts were a regular diet. Tubers and roots would be found all year round, but I would guess Nuts have a season. I don't believe HGs could keep their excess stored for long.
I did understand from the article that they preferred Meat > Nuts > Tubers. This would prevent Nuts from being stored for long. I don't think that preference matters as much as actual ingestion of the foods.
I would think the best foods for humans would be Meat > tubers and nuts > leafy veg > berries > other fruits. Fibrous vegetables that can be eaten raw, would probably be better than fruits.
I am ambivalent about fibrous vegetables, that cannot be eaten raw, as they require utensils. This would make them a neolithic food. I think they are OK when cooked but I am not sure.
This means that Nuts should be OK in large quantities for use in meals. So almond meal would be OK, and I would guess so would be unrefined potato meal. I don't think cauliflower meal is a good option.