Derek,
I have actually use a similar technique myself, except that the first cut was made with sharp scisors to reduce stress on weakened blistered segment. I then inserted a piece or vinyl flooring into the blister and pressed down onto it so that the edges over-lapped. A sharp knife was used to cut through both layers of the overlap to produce a perfect mating. (The vinyl was there to protect the backing).
The remainder of the repair was as you described.
I did not sugest this to Clair because if the repair turns out unsatisfactory she is on her own, whereas an 'accidental spillage' should be covered by household contents insurance.
Sorry, Clair, if I assumed that you may not be sufficiently competant to conduct the repair.
John.