You will certainly find that you can play it faster and easier using method B - i.e. approaching the thumb to the black keys and simultaneously moving back the fourth finger.
N.B. This method should be used wisely and occasionally only, because position B is obtained by the abduction of the hand and/or adduction (rapprochement) of the elbow, which is not always recommended.
The difficulty in using the third and fourth fingers is caused by the linking between them. We can observe this weakness of our hand when trying to straighten out the fourth finger while keeping the third completely folded. The explanation is that the tendons of the third and fourth fingers cross at the wrist, which makes them inevitably dependent.
This morphological obstacle has also been known in piano playing for a very long time. Chopin already taught that the fourth finger is the weakest one and he called it a “Siamese twin” of the third finger. There even was a pianist who had that particular tendon cut surgically - of course, and unfortunately, with catastrophic results.
We can avoid or at least considerably reduce this inconvenience by using the above method. However, it cannot be used universally, but only in very difficult pieces like, for example, the chromatic Etude (Op. 10 No. 2) or “Double Thirds” Etude (Op. 25 No. 6) by Chopin. Still it is useful to keep this technical solution in mind and apply it if necessary.
Of course, pianists with an inborn technique apply this method in an instinctive way and so they do not teach it. It's a pity, because in general it is better to learn consciously than instinctively. Besides, tracking the position of the fingers on the keyboard works and it is useful even in easy pieces and even when the 4th finger is not being used. Here is an example: the uncomfortable LH accompaniment in “A Tear” (“Une Larme”) by Mussorgsky will become easier and more stable when played as indicated below (fingers 5 and 1 hit the white keys at the same distance from the black keys):
NOTE! This method is only a small element of a whole arsenal of technical means that a good pianist must possess. But even the best position of the fingers on the keyboard does not help by itself without a solid technical basis.