That's pretty much the nature of fondant. I like the flavor of the MMF but I don't care for the texture. All fondant I've ever eaten has had the same type of texture. The easiest way to cut through (at least for me) is a very sharp kitchen knife. My serrated knives just tear it up. When I serve fondant cakes about half the people eat it and the other half just peel it off. It's really more for a pretty look than a delicious taste.
Add a Tablespoon of Glycerin. That tend to help some. 
A couple days ago I experimented with MMF. I like my usual recipe, but this time I tried vanilla rather than lemon, and it tasted much better. As far as texture goes, I varied the amount of powdered sugar in each one a bit. I found that when I added more sugar, the texture was better. Not quite as chewy or gummy, but it was a little stiffer. With less powdered sugar, the taste was better but the texture was very gummy.
You just have to hang in there because not only is there personal preference in texture and taste but the weather and what ingredients you use can even affect it. For instance, change up your marshmallows, confectioner's sugar or shortening for another brand and it may act differently. Or, is it raining or dry outside? I know that for me I have had to learn how it should feel to be that right balance of being strong enough not to tear but then not so dense it is too chewy. There is the play between the confectioner's sugar and the shortening to get it just right because some days you need more of one or the other.
Keep playing with it! HTH
Would it make a difference if I let it cool to room temperature on its own rather than microwaving it?
Not quite sure what you mean here. After making it, it is best to Crisco the outside and double saran wrap it and let it sit at room temp overnight. I know some people refrigerate it overnight after making it, then let it sit on the counter until it comes to room temp. I don't know whether or not microwaving it would contribute to the texture being chewy. Microwaving it in 5 sec increments is just supposed to help with pliability, and I have never heard of bringing it to room temp by microwaving it. I had some MMF turn out rather chewy, and I believe it's because I didn't use enough ps.
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