Well, I only use blender on occasion…
But simply by re-importing an exported mesh you can easily verify that morph targets are being exported. If Maya/Max don’t import them, maybe there are plugins or something? You probably have already tried all the import options. All I know is that .fbx isn’t always .fbx, like with most file types. There are also a billion converters for different model formats to be found on the web. But trying to achieve something that way can be pretty frustrating.
Otherwise, don’t know, sorry.
Thought I might help, because I have been working on skeletal meshes for about 2 weeks now, manipulating vertices, bones, morph targets (…) - but all within the engine.