I'll say that for sake of argument, but just know that I DON'T believe this to be true because how on earth could you ever have B-G twins, Gosselins, etc if this was the case?
I think that the weight loss, eating lower protein and lower fat, and PT or SP would lower T levels both in blood and in the egg. If you were sold on that idea, you should do SP for at least 3 months before TTC because that is the lifespan of the egg (it goes from a tiny "seed" to being fully developed in that time) You may even want to take the SP nonstop for a month or two before switching to AF-O when you TTC.
We have some evidence that shows that licorice + white peony has been proved to lower testosterone at the ovary itself (these supps are really hard to get unless you go to a Chinese herbalist and they may not be willing to give them to you without examining you and seeing if you "need" them). Point being, since we do know that LR and WP do affect the egg, it seems reasonable to assume that SP would too. Also people with PCOS have good results with SP.
All that having been said, until someone PROVES to me that levels of testosterone in an egg are a) present b) attracting Y vs. X sperm, and c) can even be affected by diet/supps/blood levels of T, I am going to stick with my theory that T levels improve and increase EWCM and good CM plus possibly the alkalinity of that good CM, along with some communication between sperm/numbers of sperm and/or changes in capacitation/ability to penetrate an egg shell, makes it more likely that Y sperm or X sperm are the ones to fertilize the egg.
Re left sided vs. right sided ovulation, yes, for some reason left sided O ~MAY~ yield more girls. We have no clue why and there is a lot of misinformation out there and badly drawn conclusions about this (there are studies that are already linked on this site but for some reason they are eluding me when I try to look them up and I just don't have time to hunt till I find them.) This DOES NOT mean that you can only conceive a girl from your left or that if you did conceive from your left, it would then be a girl. The interesting thing is, when you are the most fertile, you tend to O from your right. Most people o from their right the majority of the time (the idea that you alternate between ovaries is totally untrue even if it was told to you by a doctor.). When you're less fertile, you tend to O from your left.
So it may very well have nothing whatsoever to do with right vs. left, it's more fertile vs. less fertile and the side of ovulation may be totally coincidental to that OR it may be that unless you reduce your fertility to begin with, you'll just go on always ovulating from the right side, never from the left!! The fact is that people who go HT remove eggs from both ovaries and end up conceiving both boys and girls with those eggs.