Woodworking

Can anyone tell me how can I flatten a Minecraft heart please? I've put this together:

https://www.instructables.com/MineCraft-Heart-wood/

but I've noticed that it bows slightly. I've managed to get the ends to raise slightly when I've screwed it together. The top needs to be smoothed too, as there are some small differences between the pieces. Both sides are only off by a millimetre or two, but it's enough to be noticeable.

My thinking is to clamp it down at the centre, which seems to be mostly flat on both sides, then sand the top until it's level, then flip it over and clamp the edges to smooth the bottom.

Are there any likely problems with doing it this way, or is there a better way of doing it? Thanks in advance :)