How to bake object with cloth simulation and subsurf (not applied)? Having trouble using .mdd method I need to transfer Blender scene with cloth simulation to Maya and Houdini.

In addition to cloth simulation, I used subsurf (not applied), after cloth modifer. And if I apply the subsurf, the cloth simulation will change, while I need to export to Maya an object with exactly the same animation that I have now. 



I have used this method to export .mdd: http://blenderartists.org/forum/showthread.php?387461-Bake-Cloth-to-game-engine 

and I faced a few problems in the process. I used a simple plane with cloth sim to demonstrate them:


1) If I export .mdd of an object with a cloth simulation but WITHOUT
subsurf, and then, after export, remove the cloth simulation and
import .mdd - everything is OK, but the object increases in size:


Before importing .mdd:


After removing cloth sim and importing .mdd:



2) If I export .mdd of an object with a cloth simulation AND WITH
subsurf (not applied), and then, after export, remove only
clothsimulation and import .mdd - I get a highly distorted object.
And even if, after export, I remove them both - cloth simulation and
subsurf, and then import .mdd - the result is the same:


I exported as .mdd this model with cloth sim and subsurf (not applied):


This is what I get after removing cloth sim and importing .mdd:

And the same result, if i remove both, cloth sim and subsurf before importing .mdd:



3) And the third problem is that I can't apply subsurf to the object
with the shape keys, so even if I did not have those problems, which
I wrote above, I could not apply subsurf thereafter.




How can I fix these errors? I really need to export my work to Maya.

Thank you very much in advance!
Enable the .mdd file importer / exporter addon:

Select an object with the cloth simulation and subsurf (not applied). CTRL + A - apply rotation, scale and location. Note that if some other objects, which are parented (or vertex parented) to that object, after applying operation, they may change their position and rotation. To avoid it, unparent them (ALT + P - Clear Parent), before applying, then apply rotation, scale and position, and then parent them back.
While the object with ththe cloth simulation is selected, export the .mdd file. Export may take some time.
After  export - remove the Cloth simulation.
Unparent (ALT + P - Clear Parent).
Apply subsurf.
At this stage, I usially re-applying rotation, scale and position, just in case - (CTRL + A).
While the object is still selected - import .mdd file.


Play the animation, or select a different current frame to update the final result. Note that the shape key animation rather increases the size of the project.



Many thanks to  Mr Zak, m.ardito from blender.stackexchange.com and to Richard Marklew, benu from blenderartists.org for their help in finding solution!