My take is this: As long as your rendition sounds musical and does not somehow violate the spirit of the song, anything goes. If you want to get extra-experimental, that’s what side projects are for.
That having been said, since neither you nor I have ANY stake in the royalties accruing to the covers we play, neither do we have any stake in delivering them note-perfect. But we DO have to be true to them as far as giving a compelling, listenable, coherent reading of them, or else few will recognize or feel what we’re bringing.
Not to put too fine a point on it, the original artists rarely play their popular songs with note-for-note fidelity, but they would be foolish to play them in ways that are not instantly recognizable.
A song and/or performance can be outstanding without being a clone of its source material. That’s what makes a performance. Ya always gotta remember that this is showbiz.