My BM Bone White color came out very well in SW Pro Classic Enamel. We used that in our kitchen (the painter's preference) and I know it is a good match because everything else in the house is the actual BM Bone White. Just about to do what you are asking about for our MB cabs--BM White Dove, but using SW. I am not worried, at all. Since White Dove is such a popular color, I'll bet SW mixes it frequently. Maybe they already have a formula in the mixing computer so they don't have to "read" it. I would make sure to have a bit more than you need mixed up, then combine cans, just to be sure....

There is an online program EasyRGB that lets you compare one company's colors to another's. The three closest Sherwin-Williams matches are: SW2835 Craftsman Brown (nearest), SW9108 Double Latte, and SW9093 Nearly Brown.

"One also mentions an ultra white base. I’ve heard base can change the tint." Absolutely can and does make a huge difference. That is why if going with your method of buying it a gallon at a time, you absolutely need the same paint line and have started with the same base. Even then there is no guarantee that the colors will match perfectly.

https://www.myperfectcolor.com/paint/437654-glidden-30bg49047-canadian-sky-blue