You just answered your question. You MUST go with backer board or cementious board. the stuff you mentioned is no good. its a composit and it hates water it will melt and cause more problems.
Now, if the additional height is that much of a problem and in some cases it is, consider taking out the sub flooring and start up again using backer board to obtain the height you want.
If this is going to be a "high traffic" area with dogs, snow, water, snow, water, and more water, you must do this right, and thats from the sub floor up.
think of re sale value when having and building one floor heigher that the other, this is not good and could cause an accident.
You need to re group and think this out more and come up with more funds and do this right.
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