I don't have a satisfactory answer and I'm not sure that someone could give you one. Nevertheless, I want to make a few remarks about your very important question.
The effective lagrangian of Matrix theory has no potential. Also there is strong evidence that no effective potential between supergravitons can be easily generated; terms quadratic in time derivatives are not renormalized, terms quartic in time derivatives appear only at one loop, and for supergraviton bound states $N$ >2 there are terms in the effective Lagrangian which receive only an exactly computable one loop correction; none of them produce an static potential among supergraviton bound states.
See https://arxiv.org/abs/hep-th/9806081 , https://arxiv.org/abs/hep-th/9905183 , https://arxiv.org/abs/hep-th/9710104 and https://arxiv.org/abs/hep-th/9803265.
All the above is just "empirical" evidence that Matrix theory fundamentally refuses to produce such class of term in his effective lagrangian, I suspect that the reason behind this is supersymmetry. Static potentials among supergraviton bound states are usually generated in situations with broken supersymmetry, usually leading severe inconsistencies; see the very interesting nonsupersymmetric matrix orbifold. Recall that in string theory, the absence of supersymmetry produce time-dependent and tachyonic situations where is not clear that a truly sensible and complete quantum theory of gravity must exist. In the case of Matrix theory (and matrix string theory) it seems that a static potential between supergravitons may violate the cluster property of the supergraviton S-matrix in some way.
Perhaps matrix theory is just signaling an instance of the apparent need of spacetime supersymmetry for fully consistent general quantum theories of gravity.
