I would say that a deep inhale/full exhale/inhale again every two seconds (26 times/minute, as you say) is not ideal. The reason for a high flow rate is if your regulator can't keep up with a preferable breathing strategy, but it feels here as though your regulator is dictating your strategy. While people develop strategies that are customized to what works for them, I would say (as it says above) that the most basic, or maybe "standard," approach is to start with a full exhale (with crunch), then a deep inhale, then hold for a couple of seconds, then a very full exhale, and repeat. This is going to take roughly ten seconds. If this technique works for you, you might be able to use a lower regulator setting for that pace and the bag will be full when you're ready. I think this video -- https://www.youtube.com/watch?v=PtFHRIQN17s&t=5s -- is quite good. You can start at around 7:30 in the video to see the breathing technique.
I'm imagining that you have to "go lay down" after five minutes because you are practically hyperventilating, but taking a break while using oxygen doesn't seem like an effective strategy.
Let us know how things go.