The question in the title is obsolete now.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.