Perhapsman, peanutphobia and I were talking about the viability of egg lay in this MU. I have yet to thoroughly test it, but from what we've theorized, DJC egg lay and other surprise egg lay maneuvers may be really beneficial in this MU. Of course, it can't be too predictable, but egg lay might be extremely helpful in the neutral as a mixup, as Yoshi can use it as a pseudo grab in the air, and tack on free percent. It doesn't leave him as vulnerable as regular grab, allows Yoshi to snag Peach out of her float height, and also puts Peach in the air above Yoshi, which is arguably the best position to be in. A really good mixup I see aMSa utilize is
shield drop --> DJC egg lay, or even a b-reverse variant of djc egg lay.
Positioning vs. Peach seems to be best at a diagonal away from her when she is floating above you, as it is out of her float cancel nair/fair range, and gives you options to bait her moves and go in. It is also good for Yoshi to be directly below Peach when she is in the air, as she has bad aerial priority underneath her, and Yoshi can cover this with his invincible head on usmash, and juggle her with uair.
I've found the most success in this matchup playing a runaway egg camping game, as it seems peach has a hard time maneuvering through egg toss if she can't handle it properly. Then again, camping eggs gives her plenty of time to pull turnips, but they don't seem too terrifying with parry and djc armor. Still, this is a painful and oftentimes long and strenuous MU, and Peach definitely has the advantage. If we could give this MU a good crack (ha! eggs. crack... yeah that was bad) then I would feel a lot more confident.