Note: This post is way out of date, expect a new one soonish.
Apply the mirror modifier
Hit apply on your mirror modifier. Be careful: further changes will not conserve our precious symmetry! I advise that from this point forward you refrain from saving your work, or at least save it in a separate file.
Rotate the model
We’re going to do the rotation using hotkeys. This makes it easier since you’ll need to do this for every model.
'R' (rotate) '9' '0' (ninty degrees) 'X' (along the Y axis) 'CTRL'+'A' (Apply)
Then another transform:
'R180Y' 'CTRL' + A
Next you need to install the babylonjs exporter. There are instructions here. Then export the scene. .babylon is a JSON format, so you can now hand-edit anything you’d like into it, such as the proper texture file. Note that on my machine the exporter crashes Blender but does do the export.