To overturn the probate granted in the Archdeaconry of Middlesex, application would have been made to the PCC, as a higher court (as mentioned above).
As the beneficiaries named in the written will were effectively excluded from the later, nuncupative, will, there may have been a dispute. But there are relatively few contentious probate records held in the PCC before 1600, so I wouldn't hold out much hope of finding anything, unless perhaps there is more in the relevant London Archives file. But if this is a notable and well documented family, as suggested, the relevant search may well have been done by someone else already.
