11d ancestor of fully E8-gauged 3d supergravity?

Question

Ever since around

• H. Nicolai, H. Samtleben, Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions, JHEP 0104:022,2001, hep-th/0103032 

it is known that there are many maximally gauged supergravity theories in 3-dimensions which do not arise as KK-reductions of 11-dimensional supergravity. In particular there is a "maximally maximally gauged" case with full local \(E_8\)U-duality gauge symmetry. A slightly more recent review of this state of affairs is in

• B. de Wit, H. Nicolai, H. Samtleben, Gauged Supergravities in Three Dimensions: A Panoramic Overview, arXiv:hep-th/0403014

Given this, it is natural to speculate about other "corners of M-theory" in 11d which would serve as KK-ancestors for these exceptionally gauged 3d SuGra-s, and of course the authors of the above articles do mention such speculations, notably in section 7 of the first hep-th/0103032, which ends with:

The only way to achieve this appears to be via a CS-like action in eleven dimensions that would encompass all degrees of freedom, and thus unify the Einstein-Hilbert and three-form actions of the original theory.

My question is if this issue of an 11-dimensional ancestor of the exceptionally fully \(E_8 \)-gauged 3d supergravity has been picked up again later?

I should maybe say that I am aware of the more recent exceptional generalized geometry-formulations (of suitable spacetime-decompositions) of 11d supergravity,such as Godazgar-Godazgar-Niicolai 13 and Hohm-Samtleben 13 ,but (unless I am missing something), to the extent that these "just" reformulate standard 11d SuGra such as to make manifest the 11d origin of the ungauged U-duality groups that otherwise are visible only after compactification, to that extent these formulations do not address the above question of what an uncompactified ancestor of the "maximally maximally gauged" 3d supergravity might be, do they?

I am aware that there is not going to be some slight variant of 11d SuGra, so that possibly the 11d ancestor of that maximally locally gauged 3d supergravity might be some rather different looking "corner of M-theory" and likely it's out of reach. Nevertheless, since the question has been kind of compelling and has been around for a while, maybe there have been some ideas since?

[edit:  I see now that in section 6 of  de Wit-Nicolai 13 there is the suggestion that the "missing" degrees of freedom in 11d to account for the extra U-duality gauging after compactification may be sitting in a non-perturbatively dualized graviton field of sorts.]