This will work. For the little extra cost and the ability to have a neutral at switch B I would still run a power cable up the stairs with the switch cable and get the neutral. I would also put a double box there and have the B switch on one side and a duplex outlet on the other side making use of the power cable. At least in every house I have owned the top of the stairs needs a nice place to easily plug a sweeper in.Since the power is coming into the Switch A box already and there is a cable BW/g going to the light from there then the common screw on switch A should have the "power in" black wire. Then run a BRW/g cable to the new switch location switch B. At this common screw connect the black wire to the common then on switch A "location" take the black wire that is going to the light and connect that to the black wire coming from switch B's common screw then just connect the two other travelers to switches A and B. The neutral connections in switch location A should not be changed. They can remain wire nutted together. This seems to be the easiest solution.
There should be a neutral at switch B by code only because now so many people are using smart switches where many of them on the market requires a neutral. Not having a neutral at switch B location is not a safety factor code violation.