Hey friend you can probably get away with the dish move IF you plan ahead.
I have several dishes mounted on home made pallets. A few months ago I moved one of the pallets / dish more than 50 feet without signal loss.
What I did was after marking the dish / mast itself with sharpie marker, I also marked the pallet orientation by way of compass with sharpie.
Picked up pallet, moved it out behind shed, put compass on pallet and rotate to correct alignment, reattached coax, TV.
Plan ahead. Make sure it's working as desired before move.
To move your dish those four inches I would put my cell phone in compass mode on the lnb arm to get a rough reading. Drill, move, re-measure with cell compass. Adjustments will most likely be obvious and minuscule.
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