As to your first paragraph: I think it is overwhelmingly likely to be true. Assuming, of course, that women have historically had any sexual agency at all (remember as I said that you only need the slightest of fitness advantages plus enough generations to pass to eventually find "fixation" of that allele in the population).
Chimps may not be "picky" but alpha chimps father many more babies than those slightly lower in the hierarchy let alone the Russell Greer style chimpanzees. See above. The lucky but less-fit chimpanzee who sneaks a fuck and contributes his genes to a new baby will, ten generations down the line, likely have no descendants. But your point about chasing away other males, etc. is well-stated and explains animal sexual dimorphism where males get increasingly scary-looking or powerful. Evidently, the benefits of a powerful Neanderthal-type physique were insufficient to justify the cost in humans.
As to your second paragraph: I may well be mistaken but I genuinely don't see how it follows from the first unless there's an idea missing somewhere. I do agree with what you at least imply, namely that rainforests probably aren't cognitively demanding environments. But why would a more cognitively challenging environment without that readily-available abundance of food move us away from gorilla-like mate-guarding? It's not like they're practicing family planning. Perhaps you're suggesting (and this is an idea I would agree with and in fact has a lot of support) that this type of hardship drives the creation of small families with intense interfamilial bonds: no longer can the village raise a child.
I was not familiar with the gorilla stats! Thank you. But the huge time commitments of the gorilla diet are probably more down to the fact that they are eating extremely low-calorie fibrous plantstuff -- absurdly large amounts of it every day to extract its meagre energy. And they need to walk around with not only huge amounts of rotting shit in their guts but have huge metabolically-expensive intestines. Gorillas, unlike humans, can get energy from cellulose; like humans, however, they only have the enzymes to break down carb's alpha glyosidic linkages and not beta linkages like in cellulose so rely on bacteria to do so which takes a while and involves a very long transit time, a huge long metabolically-expensive intestine that gives every gorilla and absurd beer-belly look, and I imagine lots of farting. I'm sure a gorilla could gorge 11,000 kcal in two short takeaway meals, if offered. Also the gorillas I've seen clips of eating seem to do so in an incredibly languorous, lazy manner, almost meditatively as they stare off into the distance, passing wind. It's not like they have anything else to do.
Thank you for saying "sapient" not "sentient".