Is there a simpler way to say 平行支持鏡 Heikō shiji-kyō? It means parallel support mirror?

Yes, you could. Because parallel means 平行, a term which is easily
understood and commonly used in Chinese.
Support means 支持，mirror means 鏡. This two term, are same as before, are easily understood and commonly used in Chinese.
Pillar means 柱, means something which has a function strongly support something above it. Ex, traditional houses in some areas, or houses in flooding area, house is constructed above some pillars; and as far as I know, the number of the pillars is just 4, right?
So, it depends on the shape of your device, both 平行支持鏡 or
平行柱鏡 is easily understood, and it’s much easier than “Rasengan - spiraling sphere" to translate.
And, for a new device, you actually can give it a fancy name, like Lightsaber in the movie of the Star Wars. We translate it into 光劍.
To name new device out of box is totally no problem. And 平行支持(柱)鏡 is also a fancy name, but sounds not very fancy.