Hi Alison,
Thanks for posting your games. They are very interesting.
One angle you might want to consider is the study of tempo. That is usually a key in winning advantageous positions.
Notice how many times in the Petrosian game you posted, he takes or threatens forcing the opponent to react defensively giving Petrosian a tempo move to increase his advantage.
In your tough Sicilian "trick" loss, White's tempos gained after 9. Bxe6 seemed to end up painfully strong.
Some good resources on Tempo or Time might be Evan's "New Ideas in Chess" chapter 5 (which is my go-to book) though I've seen some good stuff from Silman and, if I remember correctly, the original (which I always thought influenced Fischer, a master of tempo) Nimzowitch "My System" deals with it pretty well.
Play the Petroff against 1) e4. It quickly puts your opponent into "your system" and will save you lots of headaches in the opening.
The theory is quite large, and many positions rather sharp, but that's what you open yourself up to whenever you respond with 1)...e5
At least the Petroff reduces the theory you need to know by a very large factor.
Besides, "openings" are a largely a waste of time below USCF 1900.
Study the other phases of the game instead. You will see a much bigger payoff for your game results, and for the speed at which you can comfortably play.