In the review by Hooke (1981) it also seems clear that laboratory and field experiments yielding the empirical constants $A$ and $n$ diverge. One reason for this is that small laboratory specimens of ice yield values that are not fully representative of natural conditions.
So, the final comment is that using a single value of A is a last resort when the complexity of the natural ice cannot be accommodated in calculations or models. The value of $A$ is still site specific and not generally transferable between glaciers or sites on glaciers. In the end the use of solution for the flow law depends on what is "good enough" for the problem to be solved.
References
Alley R, 1992. Flow-law hypotheses for ice-sheet modeling. Journal of Glaciology, 38(129), 245-256. doi:10.3189/S0022143000003658
Glen JW, 1955. The creep of polycrystalline ice. Proceedings of the Royal Society, Series A228 519–538. https://doi.org/10.1098/rspa.1955.0066
Goldsby D, 2009. Superplastic flow of ice relevant to glacier and ice-sheet mechanics. In Knight P, (ed.) Glacier Science and Environmental Change. Oxford: Wiley-Blackwell, 527pp. https://doi.org/10.1002/9780470750636.ch60
Gow AJ and Williamson T, 1976. Rheological implications of the internal structure and crystal fabrics of the West Antarctic ice sheet as revealed by deep core drilling at Byrd Station. Geological Society of America Bulletin, 87, 1665–1677.
Hooke RLeB, 1981. Flow law for polycrystalline ice in glaciers: comparison of theoretical predictions, laboratory data, and field measurements. Reviews of Geophysics and Space Physics, 19(4), 664–672. https://doi.org/10.1029/RG019i004p00664
Millstein JD, Minchew BM and Pegler SS, 2022. Ice viscosity is more sensitive to stress than commonly assumed. Commun Earth Environ 3, 57. https://doi.org/10.1038/s43247-022-00385-x