The pieces of my cutting board have a square 6/4 cross-section. I sawed them out, flattened two faces with a #7 and ran them through a lunch box planer. The same thing happened with both of them: I got smooth surfaces on the flat sawn sides but tearout on the other two sides. I think this occurs because this is mostly the axis where the grain is reversing. It didn't make sense to me to take it out before the glue-up because there would inevitably be some flattening required. I also didn't think it made any sense to try to flatten it until the edges had been shaped so surfacing the cutting board became the last step.
The first, unsuccessful time that I tried to flatten the cutting board I used a hand plane because I was thinking about something I had seen in person. I once watched Graham Blackburn fettle a Sears plane he got at a garage sale and then plane beautiful, wispy shavings off a piece of maple, first in one direction, then the other and finally across the grain. It was amazing and I was very impressed. Doing this obviously requires that the plane be very well tuned-up and adjusted and that the blade be extremely sharp. I really wanted to do this so I spent some time getting my Millers Falls #4 ready to go. I used the bottom of the cutting board for the experiment and had fairly good success, although I did produce some, quite shallow tearout and it was somewhat tedious because I was taking extremely thin shavings. I am not sure whether this was because I had more difficult grain to work with or he had done a better job with his plane or both.
The obvious tool to use for this purpose is a cabinet scraper. By coincidence, between the first and second time I tried to smooth my cutting boards, I watched Paul Sellers make a cabinet door from sapele. He encountered reversing grain and stated flatly that there is no plane in the world that could smooth this, not bevel down, not bevel up, not low angle...no plane period. This may be because he was working with sapele, but, in the case of maple anyway, I knew first hand that it wasn't true. Nevertheless, I turned next to a cabinet scraper, the tool he used. For no good reason, this isn't a tool I reach for very often. This time, I took some care with preparing and adjusting the blade, using a piece of notebook paper to set the depth. I got good shavings that were about as thick as the ones from the plane and there was no tearout. Like the plane, removing the tearout was tedious.
There are other possibilities. I have the Lee Valley low angle smooth plane and a blade with a 50 degree bevel (resulting in a cutting angle of 62 degrees) that they say is for working difficult grain. I tried it on a piece of scrap maple that was badly torn out and was happy with the result, barely distinguishable from the surface created by the cabinet scraper. The process was much faster because the shavings were thicker than those from the bevel down plane and the cabinet scraper.
There are also scraping planes and, while I don't have one, they may well be the ideal tool for this purpose.
The bottom line for me is that next time I will use the low angle smooth plane with a 50 degree blade followed by a few strokes with the cabinet scraper if necessary. The higher cutting angle of my bevel up plane definitely made a big difference. It is quite possible, of course, that my results would have been different if I had used sapele.
I am thinking about making a kitchen work table from maple and just have to decide whether I am willing to put up with all of this on a large workpiece. One thing is for sure: if I do it I will spend a whole lot of time on stock selection.