"added...OR someone has to find another Katherine married to a.n other Eastwood"
I found no other marriages for a Mr. Eastwood to a Katherine in the SMI.
But how can we be sure that the JOHN EASTWOOD baptised 12th August 1706 died 1800 Mayfield.
married KATHERINE PEARL 26th December 1726 is the son of JOHN EASTWOOD born 1679 died 1743 Mayfield married 26th October 1704 St Dunstans Mayfield to ANN PIPER born about 1676 in Mayfield ?
Equally it could be John Eastwood who married Elizabeth Pet 1739 who is John Snr & Ann Piper's son if there are two John Eastwoods's?
Have I missed the conclusive evidence somewhere? reni 

Drowning in a sea of tears and frustration here. The simple answer is we cannot be sure...
Howsomever

we can make an edumacated guess

The John born 1726 would have been 20 at the time of his marriage to Katherine Pearl, a more usual age for a fellow to be going up the aisle! And he was born and married in Mayfield. So he' is the better candidate to be the son of John and Ann Piper.
Now; as we don't have evidence for another John anywhere we can only surmise his age at the time of his marriage to Elizabeth Pet but I usually go on 20/25.
I think that's why folk thought he was the same John marrying for the second time to E P because he'd have been 33, plenty of time to see off one wife and find another....also the absence of any baptisms to John and Katherine, I think we simply thought she'd died..
Also, although Elizabeth Pet was said to come from Mayfield...John was not similarly described...the marriage was in Withyham which makes me think he is a different John
Shut me up someone, I'm waffling now

Suey