Tire should be replaced. It is worn thin, and you will get more and more flats. Unless your time is worth nothing, or you are enjoying this, or you literally don't have $25, it is time for a new tire.
I never noticed a flat rate difference as tires with protection layers (like the GP4000) got thinner. That disappeared when I moved beyond tires lacking aramid layers.
This GP4000S worked as well as new for the first 1037 miles up front followed by 5257 in back.
My current pair of GP4000SII tires with 6025 and 3913 miles are doing well too. Only two punctures come to mind - one where a tube cracked producing a slow leak under a sticker put there by the factory, and a second from a nasty thorn which would have gone through anything short of a Mr. Tuffy.