Here is what worked for me. I used my laptop, zoomed in a bit on the images and brought the screen fairly close to my face. I ensured that the image was crisp using each eye (I also have astigmatism, and I probably also need reading glasses, but there is a sweet spot where both eyes have good focus, and I ensured I was there.) While crossing my eyes a bit, I start to see a third image in the center of the two images, but it's either out of focus (like two overlapping images), or it's very thin, like it's not the full image. I relax and keep my attention on this imperfect image and try to focus on it without trying too hard. Using this approach the image suddenly comes into focus and I no longer have to try to keep it there.

I feel like the key might be to notice the very beginning of the desired image in the center and then to try and focus on it, but in a bit of a relaxed way.

Incidentally when it works it is extremely weird! The other images essentially disappear and it's like you've travelled to another dimension.

Optician used to tell me to work the muscle by following my finger to my nose, trying to maintain a single image. At a certain point it will snap into two - the 'lazy' eye has given up and drifted slightly - the goal is to get the finger as close as possible. Obviously if you get very close or all the way, that's 'cross-eyed', but I just can't do it.