You don't think there is a possibility that such mass exists? Or that the conditions that accompany the mass would result in such an occurrence?
As to whether such a theoretical mass may or may not exist, I don't really care to argue. (But a theory that relies on the existance of such a thing strikes me as silly). Mainly for this reason though, I do not deny the possibility that such an exotic particle may exist as some have theorized with a negetive mass, which as far as I know is allowed by General Relativity, but such a particle IS specifically denied be a posibility in the Standard Model. If you are claiming that a particle with a negetive mass, or any form of particle that is not affected by gravity, exists, then it is your responsibility to show some evidence that such a particle exists.
So far, no astrophysicist has been able to show that these things exist anywhere, or show that such a phenomenon occurs, so as far as this argument is concerned, unless the existance of such matter can be established, there is no reason to belive such particles occur in nature and therefore not a valid argument for you to use.
Secondly, even if you theorize that the mass below the mantle is made of a "gravitationally neutral matter", what of the energy that is supposedly accelerates the Earth, and the immense gravitational field it should produce. This does seem to violate the principles of general relativity in this case (the energy required to accelerate the Earth). Theorizing that the mass under the mantle is gravitationally neutral solves only part of the problem you see, unless you want to argue that it is also some kind of impossible "gravitational buffer" that prevents the gravitation of the energy under the Earth from being felt.
These are the reasons I think UA is flawed and this site would do well to adopt a theory to argue that does not require it.