Probably wouldn't hurt to try a friends bike if someone with the right size will let you borrow it. If you experience the same thing on his, it's probably not your bike's geometry.
Regarding the suggestion for plush grips. I admit I am new to biking, but I know from working with tools, a lot of cushioning can make my hands go numb faster, because I can't adjust my grip properly as I work. The cushioning tends to distribute force too evenly rather than to the strong points in my hands. Look at your saddle for example. Most Mtb saddles are pretty firm to allow the rider to distribute their weight in a way that works for them.
Which, of course, is not to say that better grips wouldn't do it, and they are pretty cheap.
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