Taking the meaning of 'sewing', Bunting relates Beauford's three terms to the harp tunings as follows in p28:-
fuáil mhór = Seldom used (raising C natural a semitone higher to C sharp) aon fhuáil = one sharp, G major fuáil bheag = high bass, or flat key
This explanation generates some perplexity to a Gaelic speaking musician. One can understand Bunting relating 'aon fhuáil' (one sewing) to the tuning he describes on p28 as 'One sharp'. However the word 'fuáil' does not mean 'sharp' and, as C# is one step on from changing F to F#, why was that tuning not called 'dá fhuáil' (two sewings)? And why is a seldom used tuning called the 'fuáil mhór' (great sewing)?
There is very little benefit to putting two sharps on the instrument to transpose, as the modal system is only raised by one string, eg, from C up to D. A fairly unnecessary tension would be placed on the strings for little benefit of pitch. If such a tuning was useful, it would seem strange that the Gaelic harpers of Bunting's day rarely, if ever, utilised it. It may have been a tuning which arose in relation to octave chromaticism, which is implied by the structure and range of many Irish tunes.
Perhaps the word 'mór' refers to the tension of tuning every C to C# on the instrument and the degree of tension or of some chromatic complexity. However, it may be that Bunting has no other source than Walker for these terms and if so, his application of them may have been entirely speculative.
An argument can be made for the reliability of his information in relation to the hexachords of Guido di Arezzo. In his vocabulary in MS34 f58r, Bunting describes fuáil bheag tuning as the 'key of G natural'. This stands against the notion of a three-fold tuning system based on keys of C major, G major and D major and instead for a system perceived as being based on keys of G natural, G major and D major.
My working model of the Gaelic modal system, the seòl slinneadh, suggests the following possibility of a relationship between an ancient hexachordal system on the harp being transposed into different tunings by Bunting's era and then described in modern terms
In reality, the key of D two sharps would be fairly redundant within the Gaelic modal system in the F# era, as the one sharp tuning and the natural tuning are quite sufficient to replicate the requirements of the Bb era.
The fuaighéal terminology makes much sense when seen as a remnant of the musical past when hexachordal thinking was much in vogue. The 'mór' in 'fuaigheal mhór' is equivalent to the musical term 'major' (bigger) and 'beag' is equivalent to the musical term 'minor' (smaller) and they could easily refer to a 'big B' (the B natural of the G hexachord) and a 'small B' (the Bb of the F hexachord).
I suggest that 'aon fhuaigheal' would be perfect as a name for the C hexachord because it contains no mutating B/Bb and is therefore 'one' in itself and stands alone.