Are you sure the top is a maple veneer? Unless it's a special, it would normally be just a basswood veneer.

Unless it's maple, (and flamed or quilted maple at that) there is no benefit in staining with a darker colour. Basswood won't absorb the darker stain in the same way and you'll just end up with a top that's darker than you intended.

As far as I'm aware, staining isn't really affected too much by temperature and humidity. To a large extent, high humidity will counter the tendency for the stain carrier medium (water or spirit) to evaporate more quickly due to the heat.

Spraying paint or lacquer is where you don't want to work in high temperatures and humidity as you are very likely to get an uneven finish with water vapour trapped under the finish and on transparent/translucent finishes, you may well get a cloudy layer. With nitrocellulose finishes and a spray gun, there are additives to help counter this, but it's best not to work in those conditions.