Pax Vobis, sedeprivationism holds that the Vatican II claimants are not true popes and have no authority to teach rule and sanctify. It holds that these men are mere designees to the papacy from a legitimate papal election, but have no authoritative power whatsoever. They are pope elects. If one doesn't adhere to this thesis, then one is not a sedeprivationist but something else.
Fr. Wathen never claimed the beliefs above regarding any of the Vatican II papal claimants. At all times he recognized them as and acted as if they were true popes. There is one section in the OP where he is speculating and saying that if a usurper did, in fact, get elected to the chair and then repented, he could become the pope. This does admit of part of the sedeprivationist thesis in theory. But that is as far as Fr. Wathen goes. Pure theoretical speculation.
There is no evidence from any of his writings, especially on sedevacantism, that prove he in any way held a sedeprivationist view of the Vatican II papal claimants. He refers to all of them as "pope" in his sermons and writings. I have read many many writings of Fr. Wathen and I haver listened to hours of his sermons. If you do so, it is crystal clear he saw JPII and previously Paul VI as true popes and based all of his defense of Tradition off this premise. Sedeprivationism holds these men to be "pope elects" and not true popes, thus referring to them as popes would be inconsistent with the thesis.
Fr. Wathen was clearly R&R throughout his life as evidenced by all of his writings and sermons. He believed we had a duty to obey the Vatican II papal claimants as popes except when they legislate, in his opinion, illegal, illicit, or unjust laws. As I said, if he were a sedeprivationist he would have said Paul VI is not a true pope with authority (at all), but a mere designee, and so none of his acts (including the Novus Ordo Missae) are binding on the faithful, end of story. In the sedeprivationist thesis there is absolutely no need to go into Quo Primum at all as Fr. Wathen and the R&R position extensively does.