However, based on the excerpts from his paper, the isochron method seems to be quite unreliable.
Sure, that is why dishonest creationists quote-mine excerpts. A true understanding of the paper and the science in general shows that the isochron method can be trusted.
Progress in human affairs has come mainly through the bold readiness of human beings not to confine themselves to seeking piecemeal improvements in the way things are done, but to present fundamental challenges in the name of reason to the current way of doing things and to the avowed or hidden assumptions on which it rests. -- E. H. Carr