Quite right about unrecognizable as a synonym for the irr form. That occurred to me after I had posted it. Dumb.

I gather that the irr form is an eroded way of saying in, with words beginning with r. So it's really "unrecognizable".

Which doesn't do anything to explain irregardless... I think it might be that people sometimes like the sound of a rolled r as a way to emphasise a word, and if you do that to regardless, it can come out as irregardless.