That looks like a great project and I see potential for success.
I will share my own experience insofar as I've never grown that plant or hand pollinated cacti.
The plants I have hand pollinated were Euphorbias and I think the main concept is the same. You want to move fresh pollen (normally the best looking stuff, think like a pollinator) from one plant to the stigma of another. Some people use fine paintbrushes, and the experts tend to have a very specific tool they prefer. I used a pretty basic cheap brush. But pay attention visually to those little granules and how they travel with your tool, and aim them at the female part that dominates the center of the flower. Smother her in their love.
In general it's always helpful to pollinate in repeated visits, or at least it should do no harm to make a few separate attempts at different times of day or whenever you're able to do the deed.
I think some plants are more dependent on pollinators, or paintbrushes, than others. The Euphorbias I was pollinating turned out to be pretty effectively pollinated by the wind, I discovered shortly thereafter, and from there on out I left it to mother nature (hit or miss as she may sometimes be). The Echeverias, Dudleyas, Aloes, and bromeliads seem pretty well served by hummingbirds and bees. After a while I retired my brush except for hybrids I wanted to make on purpose, because mother nature tends to do a great job, in the outdoors at least, with the tools at her disposal.
Proximity seems to be the best indicator of success.
Each plant is different and again, I have no experience with your plant, but in some cases the best pollen is found on the youngest (most recently opened) flowers and the most receptive stigmas are found on the oldest (before actual senescence kicks in). With some plants you look for the stigma to become slightly moist and then you know she's ready. I would think you would get the best results by experimenting regularly and often, thinking like a pollinator. I would think in your case the limiting thing might be the nice fresh powdery pollen.
When in doubt try to take close up pictures and sometimes you will see things in the frame that were not visible to the naked eye, like the whitish pollen spilling from the anthers of this ice plant I recently shot.
That's what you would want to be scooping up and moving onward, if I had to guess.
You're sure those are separate plants, and not branches on the same basal plant, right?