I've never fully understood exactly how the rules work (- and I've got a degree in maths!). So I'm not going to attempt to give you a definitive answer directly.
However last year I was in a roughly similar situation myself (as my State Pension was due from April of this year), with the online information showing a discrepancy between the maximum I might get and the estimate of what I'd actually get. I'd got some years with partial contribution gaps (in some cases needing no more than about £50 in voluntary payments to bring them up to 'full' years), so I was keen to see if making some fairly small voluntary contributions would increase my State Pension.
So I phoned TPAS to see if I could get a definitive answer. My previous experience of phoning the helplines of government agencies (e.g. with benefit enquiries) made me expect to end up on hold for several hours and then to end up speaking to a so-called advisor who couldn't answer my questions anyway. However I was pleased to get through very quickly to an exceptionally helpful guy, who could give me definitive answers to my questions straight away.
So perhaps a call to TPAS could also help in your wife's case?
https://www.gov.uk/pensions-advisory-service