Irregardlessly high?

No it's not. The word is regardless.

I realize this is a stupid argument, but like yzfguy said above, it's because people like you started mistaking it for 'regardless' and using it, so it's become an informal, improper word, but still sort of a word, but not really. Since you insisted, from Merriam-Webster (last two sentences):

Is irregardless a word?
Irregardless was popularized in dialectal American speech in the early 20th century. Its increasingly widespread spoken use called it to the attention of usage commentators as early as 1927. The most frequently repeated remark about it is that “there is no such word.” There is such a word, however. It is still used primarily in speech, although it can be found from time to time in edited prose. Its reputation has not risen over the years, and it is still a long way from general acceptance. Use regardless instead.