Definitely hit through the ball while brushing over it. You need to find your own balance in this. Hitting through the ball will give it the speed/power to go over to the other side of the table, while your brushing will give it the arch to land. The quicker you can do this motion the lower the arch will be and the ball will have more quality. I believe this is also what they use to teach a lot of young players first in China, to hit into the ball first (it will go long), to generate enough speed/power, then add spin to get it on the table. This is not so much an issue for older players though, as they're able to add power more easily, but need to focus on spin more.What's helped me is to take it even a step further. Don't even start with the BH drive, just start with the BH lob. I just try to lob the ball as low above the net as possible, make sure I can do that with good timing, kinetic chain, etc. first. Then I start adding some spin.
Another thing that helped me a lot is to not drop the head of the racket. That's because if you do that, then you'd have to bring the racket head up then over the ball, and that's just too much curving around the ball to be consistent during a match. My coach kept telling me "don't curve around the ball, just go through it!" If I just keep my racket head up high, pointing to the left and a bit up, then I can directly hit the ball and brush over/through it at contact.
Of course, everyone is different. We all have different problems in our motion, which require different fixes. Those are some of the fixes that worked for me.
This is also why many who close their racket angle more without correct timing/technique will have shots going into the net or maybe even onto their own table, because they don't hit through the ball enough