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Lawrence Krauss and James Dent recently proposed a mechanism for producing the observed scale of dark energy. This proposal was inspired by the see-saw mechanism that produces light yet non-zero neutrino masses.

I can't help but notice there are many reasons to doubt the see-saw mechanism package since it suffers from the the flavor, CP, and gravitino problems and several alternatives have been proposed.

Would it be feasible to come up with a mechanism based on the alternatives to the seesaw and hence extend Krauss' and Dent's proposal?

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I didn't read the details of the paper. However, from what I saw the authors show that by coupling a new scalar to the Higgs with coupling $\lambda_{mix} $, the theory produces a new particle with a mass proportional to this mixing. They then go on to say that $\lambda_{mix}$ could naturally be small since it should be a ratio of scales, \begin{equation} \lambda_{mix} \sim -\frac{m_H^2}{M _{X} ^2} \end{equation} This last part is where the see-saw mechanism comes in.

While analogous to it, this is not really how the see-saw mechanism works in the neutrino sector, where we are constrained about what type of new particles we can have. You could try to use similar mechanisms to ones used in the neutrino sector and apply it to this paper but this is really quite a different problem as all the authors want to do is give a natural mechanism to give mass to a new particle.

I'm also not sure that the problems you mention with the see-saw mechanism have any relevance to this new paper. In the neutrino see-saw mechanism the problems arise since we already know a lot about neutrinos. On the other hand, the paper you mentioned is talking about unseen particles which we know nothing about, so I doubt those difficulties transfer.

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