Hi and welcome!
I am not really familiar with nile, but for Machine Head I would have to go with a Miracle Man I think. Ceramic Nailbomb (Cbomb) or the Blackhawk might also be an option, but recon the MM will be rather spot on.
If I recall Machine Head use EMGs. The MM is as a guiding point sometimes refered to as somewhat of passive counterpart of an EMG. Not that they actually are perticularly close in effective sound, but they do the same job if that makes sense.
With the MM you get a great sound consisting of pronounced low mids to give it a big chugga chugga. The centermids are less pronounced, leading to some saying the PU is slightly scooped at first listen, but they are there and fill the sound up nicely and helping the MM get real character. The high mids are also a bit smoothed while the highs are there, delivering an amazing cut and helping out with pinched harmonics.
This makes for a really big sound with a lot of weight behind palm mutes which has a certain smoothness about it, while being agressive too (though not as chainsaw abrasive as the Cbomb). Thing is that the mids are a bit smoother but the highs scream at your command, so youīll never sound polite when you donīt want to, but you will have a clear and defined sound, hitting hard and fast.
The Cbomb would be a lot more agressive than the MM. Canīt comment too much on how the Blackhawk fits into the comparison exactly though, but they way I hear it described it can do this style to.
All three are great options, delivering this style each with a different flavour.
Get either and perhaps upgrade the pots to the BKP 550ks to get that little extra topend with all that mahagony.
Cheers