Does the text of the will make any reference to the need for a trust to be set up for the goddaughter? If it doesn't I think you can assume she had reached the age of majority (ie 18) by 1998 (equally if a trust was stipulated then that also tells you something about when she was born). That would allow you to narrow her birth date to between the 1940s to 1980 at least. Have you considered where the testator might have been living when he/she became the god parent? This in turn might suggest a part of the country in which to look for baptisms for Nicola. Maybe even just searching on her Christian name in a local area would be worthwhile. Provided that the baptism details for the particular area(s) are available online and you can find an image of the parish register, you can then look for the testator's details. The first place I would check for this purpose is FreeReg as their transcriptions frequently include the names of godparents whereas those on FindMyPast, for example, tend not to.
Obviously this not a trivial task, but it sounds like you've exhausted all the easy ones. By the way, don't just rely on electoral registers; check Companies House, as it's surprising how many people have been company officers at one time or another.
By way of encouragement, yesterday afternoon I received a copy of a will made in 1999 which included an unrelated beneficiary whose name and address that I had no previous knowledge of, and by lunchtime today I had her current address, her birth details, occupation, current contact details and even a picture of her, so it can be done with a bit of luck.
