Does shale rock call for a larger well diameter?
WOW, a lot to digest here between the OP and comments.  Here goes:  I have to agree with Ecnerwal, there is no reason to go with an 8&quot; casing, it would be a LOT more expensive than 6&quot;.
Drilling wells is often a crap-shoot. To minimize the risk, in my area (Western Washington State), our Dept of Ecology maintains drilling well logs for every well drilled.  These logs contain what material was removed and at what depth and the depth when water was found. You could look into it if your area maintains logs like that.
On my property I have 2 wells, about 100' apart, one is a fantastic producer, at least 40 GPM!  Not that I need nearly that much, but just got lucky.  The other well only produces about 4 GPM.
I believe that attempting to refurbish the existing well might be your best bet. Like Ecnerwal said, a low producing well can slowly feed a large water holding tank that would be pumped from into a pressure tank or even a constant pressure pump that would pump from the holding tank into the distribution system.  Constant Pressure pumps vary their speed based on demand and don't require a large pressure tank.
If I were you, I'd base my decision on any available well drilling logs in your area. Drilling a new well has no guarantees. Look at it this way: If the refurbishment of the existing well wasn't satisfactory,  but still somewhat functional and you drilled a new well, at least you'd have a backup well in case of problems with the new one.