The principle followed with respect to Priests from new Church that come to Tradition is this: (1) If the candidate himself has doubts about ordination that he would like to be resolved, and a (2) Traditional Catholic SSPX Bishop, after examining all the details of the case, decides and judges that conditional ordination is needed, then that is done.
Sometimes (1) As with Fr. Gregory Hesse, the Priest himself has no doubt. (2) A Traditional Catholic Bishop or Bishops examine the case and judge that conditional ordination, in this case, is not needed. And then the Priest simply begins offering the True Mass.
Laymen are not in the final analysis either capable or competent of passing judgment on such matters in such a way as to bind others to their personal opinion. If a layman has doubts, he has every right to seek out Traditional Catholic Bishops and Priests Consecrated or Ordained in the traditional rite. But not to presume to say that every Bishop in the new Church is invalid. That is practically heretical. As Fr. Marie has proven, it contradicts the Indefectibility and Apostolicity of the Roman Church for Her to be without valid Bishops. No wonder some who believe that false opinion, contradicting Bishops and Priests, are tempted to lapse into "Orthodox" schism.
When valid form and matter are used, presumption is for validity, not against it, unless some contrary intention is explicitly manifested in some special case. This is what will have to be judged later on. Telling Father RomanTheo he is not a valid Priest without knowing anything about the specific details of his case is a different kind of presumption. It's almost like telling a married man he is not married.
Traditional Catholic Bishops will investigate carefully before deciding. Then, laity should abide by that judgment made by the Bishops.
When a person comes to Tradition, he will receive all the graces he had thus far been losing out on. The vast majority of Traditional Catholic Bishops and Priests have endorsed that study by Father Pierre Marie and apply its conclusion in practice. We should recognize their authority and do the same.
Edit: And yes, the term for High Priesthood that is used is summum sacerdotium in Latin. That can be verified in the SSPX study itself.