My fertility doc advised to use ovulation strips and only do it when on the day of ovulation and the day after, he said that would be enough. Basides my other problems - that worked for me.
Actually I also have one tube and it's not so easy to get pregnant with one (at least for me so far). Only vary small percentage of women have tube that will pick up egg from both sides.
Also you are not ovulating left-right-left-right each month. My fertility doctor says to give it 8 months after the surgery, so I have possibly 4 positive months.
I have left tube blocked, right seems ok, at least through HSG. Now I will have laparoscopy done to have my left tube reomoved (I have hydro) and check the right one.
My doctor says that if my right tube is fine then I can get pregnant naturally, if not my first option should be IVF.
I also have blocked tube, my fertility doctor said that women ovulate on both sides, but it's random, so you can ovulate on the same side couple months in the row. Also, some tubes do grab eggs from oposite ovary (but it's rare).