The origins don’t really matter at this point. That’s what the character looks like and it’s what everyone expects.
Your use case is extremely niche. Making a font choice for that specific double-line situation would alienate everyone else who just wants the ^ to look like a ^.
Like others suggested, just use the Unicode arrows if you want arrows. Let the ^ be a classic ^.
It’s really disappointing when I find a new font that seems interesting until I encounter one weird design choice that makes it surprising to read. Fonts should be boring, typical, and follow what your brain expects to see, not trying to erase decades of typography norms and start something new for one common character.