In answer quickly to your points:-
1. The Fea’s Petrels were solely identified on range so probability. As you indicate, the last week of April is within the breeding period of Fea’s Petrel (population 500 pairs) and right at the end of the non-breeding period for Desertas Petrel (160-180 pairs). So whilst Desertas Petrel does occur in the Cape Verdes outside the breeding season, surely the combination of timing and population size makes it a very strong probability that they are Fea’s Petrels. Indeed, that would be the case even if the entire Desertas Petrel population was in the Cape Verdes at the time.
2. I think to speculate on what is the most likely taxon in British & Irish waters, you need to combine the following:-
(i) Population size – with populations of Fea’s (500 pairs), Desertas (160-180 pairs) & Zino’s (65-80 pairs), this would indicate Fea’s Petrel on size of population.
(ii) Distributions – however, Fea’s Petrel (4,000km) would need to travel twice as far as Desertas or Zino’s Petrels (2,000km) so that would suggest Desertas or Zino’s Petrel on distance travelled.
(iii) Known movements – this is where the data logger information which suggests that Fea’s do no travel much but Desertas & Zino’s do is interesting. However, as only one Fea’s Petrel chick was recaptured as an adult and the proportion of the population sampled was the smallest, surely that is of limited use? The fact that Desertas & Zino’s travel to the south Atlantic, eastern seaboard, etc with such small populations, makes them thin spread doesn’t it? So I do not really buy the theory that this study suggests Desertas & Zino’s Petrel are more likely vagrants for us than Fea’s Petrel.
(iv) Plumage/morphology – as you point out, the size of the birds, their structure and the bill means almost all are Fea’s or Desertas Petrels. The fact that there few if any birds with massive bills suggests to me that they are not adult males certainly. I chatted to the late Jimmy Steele (whilst seawatching at Newbiggin) about the two I have seen well from boats in British & Irish waters. Both conformed totally to his British Birds article.
(v) Time of year – for me the August/September peak suggests that the majority of our birds are young Fea’s Petrels. As you say, non-breeding Desertas could be the source (or even extreme foraging trips), but I favour Fea's. I doubt that observer bias is that important. Sea temperature could also play a part in the August/September peak. Wouldn’t that mean birds wandering at that time of year may wander further into our waters?
3. Struggling to find my references this evening, but surely the significant differences in size and bill make sexing in the field possible (from boats) and surely as well bill sizes increase with age (whereas overall size of the bird is pretty much fixed on fledging). I was interested by the size variation of the bills of the Bulwer’s Petrels, I saw on Madeira and assumed that this was age-related if not also related to sex.
4. I don’t know If moult or plumage could ever be useful?
5. I know of one claim of Zino’s.
On balance, I think all three taxa could occur but personally, I think that we most likely get Fea’s Petrels……….
All the best