Hi, sorry about your brickwall!
Does the will for james say where it was proved? The documents online search will only find wills which were proved at Canterbury - these would be wills from that area plus those around the country which involved property in more than one administration district (if I remember correctly).
So if John left property in one district then his will (if there was one) should have been proved in the local diocese. According to
http://www.berksfhs.org.uk/genuki/BRK/#Probate this should be the Salisbury Diocese which can be searched online here:
http://history.wiltshire.gov.uk/heritage/ Already it is getting confusing since that is the Wiltshire County archives, and you may not have thought to look there. I can see some items on there - search for
Chivers, John and see if any of the dates or places look likely. The dates are probably probate dates and so could be a while (years even) after the actual death.
West Challow is near wantage and it seems that some of the Wantage wills are kept at the Bodlian in Oxford (Wantage being a peculiar court for a while). The court of the archdeacon of Berkshire is a posibility too. On Genuki it says "Berkshire FHS in partnership with BRO, Berkshire Record Society and Oxfordshire FHS is involved in a project to index all probate documents of the Berkshire Archdeaconry for period 1508 to 1858. The first part of this work is expected to be published in 2011. " I suppose your wills would not be included in the first part though!
You could try contacting the BRO
http://www.berkshirerecordoffice.org.uk/ if you haven't already done that, and ask for their advice of where to look. Berkshire Family History Society might be able to help too. They have a disc including burial at West Challow up to 1820, I do'nt know if it would be worth looking there to get a death date?
Hope some of this is of use