The dfg conjecture for zero-dimensional interpretable groups over the p-adadics

Let $G$ be a $\mathbb{Q}_p$-interpretable group. Say that $G$ is zero-dimensional if its dimension is $0$, and definably amenable if it admits a definable invariant mean. The group $G$ has dfg (definable $f$-generics) if there is a global definable type on $G$ with boundedly many left translates.

The dfg conjecture. If $G$ is a $\mathbb{Q}_p$-interpretable zero-dimensional, definably amenable group, then $G$ has dfg.

This conjecture is suggested by the contrast between the properties fsg and dfg in distal theories such as $\mathbb{Q}_p$: infinite interpretable groups have at most one of these properties, and dp-rank-one definably amenable groups have exactly one. The source does not state a resolution, so the conjecture remains open.