A .mtlx file can be edited with an Edit Material Network node. However, this is a bit sub-optimal as the material parameters on an ND_StandardSurface come in in the wrong order and all of their values and input connections do not show. That is not the case with a MaterialX written out as a .usda file. There the Edit Material Network works perfectly.

That leads me to my question: Is there a way in Houdini to convert a .mtlx file into a native USD MaterialX material network (VEX)? Or a way to convert a .mtlx file to .usda?

There is no direct conversion from .mtlx to .usda in Houdini. The only way to to it is to read .mtlx with a Sublayer LOP (Tab > File), and then save the LOP's stage out to .usda file (eg, RMB on the LOP > Save > ...)