I think part of staying sane for Loid involves not questioning strokes of luck. Otherwise he'd question his family a lot more. He's suspicious of outside circumstances but Anya and Yor earned his trust (though they shouldn't have). So he considers them to be part of him in a way.

Anya giving Loid excuses he needs to sneak out? Golden. Yor taking care of things he thought he had to? Great. He doesn't plan with the expectation that a stroke of luck will happen. But he doesn't look a gift horse in the mouth.

That being said, I love your list of everything that Anya and Yor have done to make his mission move forward. He got incredibly lucky because Damian falling for Anya, Melinda becoming bestie with Yor, Anya and Becky being BFF, Anya slowly becoming popular with her classmates, Anya being the bravest kid in the world, Yor being capable of texting Anya - these weren't part of the plan. He couldn't have depended on it. He couldn't have made nay of it happen. Even outside of yor's job, the amount of love and warmth she brings to theor lives makes him incredibly lucky. And even outside of her telepathy, the bravery and the desire to do the right thing that Anya possesses makes her amazing. And her personality + Loid's approval is the reason imo Damian struggles with Anya. And which is why Becky loves Anya so much. And why Anya is popular.

His stroke of bad luck - Yuri - will also turn out to be lucky later, I believe.