The 4095 x 4095 image size limit is not arbitrary and, unfortunately, cannot be increased.

This is a limitation of the underlying Adobe Flash technology within JuiceboxBuilder-Pro/Adobe AIR. The largest image size which Flash can handle is 16,777,215 pixels. This equates to a square image of 4095 x 4095.

As you have images larger than this maximum resolution, then you could perhaps do one of the following:

(1) You could resize your images first in an imaging program (such as Adobe Photoshop) before feeding them to JuiceboxBuilder-Pro (perhaps resizing multiple images at once as a batch process). If you do resize your images prior to using JuiceboxBuilder-Pro, be sure to deselect the 'Resize Images' checkbox on the 'Images' tab to ensure that JuiceboxBuilder-Pro does not resize your images further.
I realize that this is not ideal but I hope that it is not too inconvenient.

(2) There are plugins available to create Juicebox-Pro galleries with other programs (such as Adobe Lightroom) which do not have the upper resolution limit of JuiceboxBuilder-Pro. You can find details of these plugins here.
If you use Lightroom, Photoshop or jAlbum, you might like to try creating your galleries with these programs as an alternative to JuiceboxBuilder-Pro.

I know that this does not directly solve the problem but I hope that it at least helps to clarify things a little.