I don’t think 63/37 flows any better than 60/40 (the advantage of 63/37 is the that it’s a true eutectic, as I explained above). Any differences will be down to the quality (purity) of the alloy and above all the flux.
Thus, I completely agree with your statement that quality is paramount.
Kester 44 is great solder because it’s a fantastic flux, and the metal is of top quality. (In contrast, I am not impressed by Stannol, because their fluxes aren’t as good, and I’ve tried multiple of their fluxes.)