With virginias, "bite free" is, to me, very much a non sequitur because the preponderance of virginia blends will bite when pushed. Virginias need to be sipped slowly.
Now some puffers have a physical aversion to certain leaf, such as red virginias. Others have a problem with certain processes used to prepare certain leaves as well. And some can't handle humectants, such as propylene glycol.
As for the Mick McQuaid blends, I don't believe there's anything quite like them.
If you're referring to the Plug, I suggest you try Peterson 3P, and the G.L. Pease virginia plugs -- Jack Knife Plug and the Triple Play. All of which greatly improve when cellared for a year or 2.
While not the same in presentation as the Mick McQuaid little square flakes, Peterson's Irish Flake, to me, is similar, but the latter contains a bit more burely and is considerably higher in nicotine IMO. Not like the Mick, but a favorite of mine, is the Peterson University Flake, which is fruity (though not nearly as fruity as Erinmore Flake). Another fine virginia flake and a favorite is Dunhill Flake.
If you can find it in stock, the Esoterica Dorchester from Germain is also a fine choice.