The question in the title is obsolete now.
But the issue
to drive the Higgs mass to the lower bound, rather than to the upper bound, in an altered version of the noncommutative standard model
remains relevant and has been addressed indeed by an updated almost-commutative spectral extension of the standard model. See http://arxiv.org/pdf/1208.1030v2.pdf and http://arxiv.org/pdf/1304.8050v2.pdf
This extension claims basically that in addition to the Higgs scalar field, there exists a neutral singlet scalar field (σ), whose vev gives a Majorana mass of at least of the order of 10^11 Gev to right handed neutrinos. This new scalar field can stabilize the Higgs coupling and prevent it from becoming negative at higher energies thus make it consistent with the low Higgs mass of 126 Gev found by ATLAS and CMS collaborations at the LHC.