Help/advice needed - cupped panels

I need some helpful advice on how to tackle a problem.
I am building some shelving out of Blackbutt to fit under the overhead cupboards in a kitchen.
I've glued up all the panels, which are 340mm wide, but because of the humidity and storms we're having in Brisbane at the moment three of the four panels have moved/cupped. The only one that didn't move was the one that was sitting flat on the workbench with another panel on top. The other three all had one face exposed to the air, and that exposed face has absorbed the moisture from the air. I really need to get these flat again, as the ends are all mitred to form a box shape. The mitres had already been cut on the top and bottom of the box before they moved, but the gable ends have not yet been cut, and that board hasn't moved/cupped.
At the moment, I have them stacked and stickered so that both faces are exposed to the air, trying to get some balance in the moisture content back into each face. Is there any better way, or anything else I can do to help?

You either need to shrink the side that swelled or expand the other side, so there's 2 options which are essentially just 2 different ways of doing the same thing - balancing the moisture of both faces.

1) Dampen the concave side and lay it wet side down on the floor; this will put moisture into the narrower face and cause it to expand. We used to do this at my old work with large table tops over night, depending on the thickness, how far it needs to move and the weather you might not want to leave it for so long.

2) Leave it dry and put it concave side down in the sun; this will dry out the wider face and cause it to shrink. Check its progress regularly because it will cup the other way if left for too long.

You can have a bit of both ways if you put the panels out on damp grass.

Thanks Elan,
Some of them had started to flatten out a bit by the end of the day yesterday, but not as much as I had hoped. I think I'll have a go at putting them in the sun, as I feel that I've got a bit more control with that, rather than trying to dampen the other side. After all, how much is too much moisture to try and introduce?

The other point of relevance: it's always a bit of a conflict between keeping clean for glue up and this option, but as soon as you have flat/square (enough!) get a coat of finish on if you can. Base coat, oil, or paint will help reduce moisture exchange... tape over joint areas if necessary to keep clear for glue. Putting the carcass together will stabilise everything considerably.

Oh, and re-reading your post, make sure you sticker raw wood so that its out of direct sunlight, and air can get to both sides... I sticker, and use sacrificial sheet goods on top with heavy weights on it. Of interest, I've made myself a thin, hardwood 'drinks coaster' that sits in the shop. It's useful to watch it cupping on the side exposed to the air on a daily basis: any side resting directly on a surface will absorb moisture differently to one exposed to the air...Turn it over the next day, and back it goes the other way... And it's oiled to saturation point!

Always a problem with blackbutt. Big, open pored timbers are always moving more. Tighter, fine grained timbers are stable. This is the main reason we use new guinea rosewood here for almost everything, it holds paint well too.

Thanks for the replies and suggestions. I managed to get everything pretty close.
I started with just putting them out in the sun, but it wasn't really happening for me, so I ended up laying them on the damp ground out in the sun and kept checking them regularly. All bar one came good with that technique. The other one came good on one end, but the other end still needed more. I brought it inside and laid a damp cloth on top of the end that still needed more, and it eventually came good too.
Huge thanks.