The difference here though is that here the baptisers don't even claim to be Christian, so even Patristics on heretics and schismatics, is of little help.
I haven't missed that.
There is valid baptism. Trinitarian. Three-times immersion in water. By a priest. With GodFather. It's required for salvation.
There is yet another case, of (I don't know the proper English term) "announcing" - in case of unbaptized who are in danger of death. Trinitarian. Performed by a baptized soul. No necessarily in water, sand can do it, or dust. If God allows and the endangered survives, baptism can be performed afterwards.
There is also "baptism in blood". It's not Trinitarian. There is no priest, or baptized soul to baptize. Yet, it's baptism, sufficient for salvation.
Mentioned Cannons referred to baptisms that aren't valid, yet, as a rule, if they were Trinitarian ones, there would be no other baptism, just a chrismation, or confession. It's applicable until today.
In all of the cases, baptized is immersed into Christ's death, so he could be resurrected in Christ's Resurrection, upon His Second Arrival. Before His Second Arrival, there is Holy Spirit.
Since Salvation is in the power of the Saviour, and Holy Spirit is here with us, it isn't competence of any mortal human, regardless his position in the Church, to declare who can't be saved. No one knows that except the Savior.
Therefore, how could we know if baptism by an unbaptized, "whom have a will to do what the Church does" would be sufficient for salvation or not?