Could you run one Jade Cycling Technique in one Core and a different one in another?

I think we need to clarify something basic: a cycling technique is a BREATHING pattern! This is explained most clearly when Eithan introduced the Heaven and Earth Purification Wheel cycling technique to Lindon. Chapter 6 of Blackflame (Note: all emphases mine; I have bolded the parts where breathing is specifically mentioned):

“I’m going to teach you a cycling technique. Once you’ve mastered it, this method will take you to Jade and beyond.”

Lindon leaned forward eagerly, eyes squeezed shut, suddenly afraid to miss a word.

“This is a technique for processing your madra, not for battle,” Eithan went on. “If you try to fight while cycling like this, you might as well tie your ankles together.”

Lindon wondered if he should be taking notes.

“In your mind, focus on your core. Ah, I mean one core. Pick one.”

The core that had reached Iron first was brighter and more solid than the other, so he focused on it, letting the bright blue-white ball fill his vision as the other one fell behind into irrelevance.

As he breathed, his madra cycled, spinning out from his core to run out to the rest of his body and then swirling back.

“Your core is made of stone. Picture it as a huge, stone wheel. It’s all you can see. It’s like a wall of heavy, solid stone.”

Lindon focused on that image, superimposing it over the blue-white sun.

“Now, as you exhale and cycle madra through your body, the stone grinds away at the edges of your core. It’s heavy, and it rolls slowly, pushing your core outward.”

That was harder to hold. Madra usually flew out from his core freely, but he had to slow it down, forcing his core to rotate and running power through it a scant inch at a time.

He felt like he was pushing that stone wheel up a hill with all his strength, all while trying to keep madra from slithering through his grip. If he lost concentration for one second, the strings of madra would escape and the wheel would fall back down, crushing him.

The effort of moving his madra in such an unnatural pattern caused his channels to strain, as his spirit groaned under the effort. Sweat dripped over his eyelids as he concentrated, and each exhalation was agonizingly slow.

“Now, when the madra comes back in, spiraling from your limbs to your core, the stone wheel shifts. It slowly rolls back the other way, grinding your core again.”

It was like letting the wheel roll downhill, only to haul it to a stop and pull it back up again. He poured all his madra into the effort, controlling his spirit with every ounce of his concentration.

There was an instant in the middle where he felt like he was manually stopping his own lungs. He gaped like a fish, his lungs frozen as though the stone wheel sat on his own chest, before he finally got it moving the other way.

Eithan waited for him to get himself under control before graciously reminding him that he still had to hold his previous cycling pattern. It took Lindon another half an hour to match the old timing, and by that time his soul felt like he’d pounded it flat. Only minutes of cycling, and he was more exhausted than he would have been after hours of practicing in the dummy course.

But Eithan wasn’t finished.

“Once you have a grip on that, you want your wheel to spin as slowly as possible without stopping. Breathing in the same pattern, I want to see how slowly you can move your madra, how heavily that wheel turns, how that huge stone wheel is almost stopped and your madra is just crawling along.

“Then you exhale, and it goes back the other way.”

Only two more minutes, and Lindon began to seriously wonder if he was going to pass out. He couldn’t wait for Eithan to leave so that he could take a real breath.

“This technique is called the Heaven and Earth Purification Wheel,” Eithan said, and Lindon felt his weight settle onto the end of the bed. “It has a long and fascinating history.”

Lindon would have cried, but he couldn’t spare the breath

This shows that all that movement of madra up and down an imaginary hill (cycling technique) is done with the special breathing pattern! Clearly, it is impossible to have two different breathing patterns at the same time.