First, is there a procedural problem? No. Forty-four Senate Republicans voted that Trump’s most recent impeachment trial was unconstitutional, but a Section Three vote is entirely different. There is no constitutional roadblock to taking up congressional enforcement of a constitutional provision itself.
Second, is the idea constitutionally unassailable? Yes. Section Three, about aiding an insurrection, relates to a judgment of Congress, not a criminal court. The House and Senate could pass a resolution that states the facts about Trump’s conduct leading up to and on Jan. 6, for example, and concludes that Section Three disqualifies him from holding office in the future.
The implications of this would be political, not criminal. It would allow state officials to call into question the legitimacy of a hypothetical Trump campaign or complicate his ballot access. Congress could approve a similar measure that permits the attorney general to render an opinion about an office seeker’s eligibility under Section Three. These are not judicial branch judgments originating from the legislative branch, and do not create constitutional problems.
And finally, is this politically feasible? It is. Congress already voted on language to bar Trump from future office. Such a section was included in the House’s impeachment article.