I wouldn't characterize myself as a partisan of the Oxford Everettian school, but I do think it is, all things considered, the most compelling interpretation available. The challenges you raise are important ones, but they are ones that the Oxford Everettians have considered. Perhaps you find their responses unsatisfactory, but these questions have been addressed, even the one of which you write, "It's the failure to ask that last question, and really think about it, which must be the oversight allowing the nonsense-doctrine of "no definite number of worlds" to gain a foothold in the minds of otherwise rational people."

David Wallace has thought about the fuzziness of Everettian "worlds", and the implications of this for our ordinary ontology. Here is one of a number of papers where he discusses this question: http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.2189v1.pdf

As for the claim that probabilities in the Everettian interpretation should be understood as frequencies, see Greaves: http://philsci-archive.pitt.edu/3103/2/pitei.pdf . The relevant section is 3.2.3, especially the part about the "naive counting" rule, which is what you propose. The rule is a bad one precisely because basing "world-splitting" on decoherence puts the kibosh on the idea that there is a single determinate number of worlds. If Wallace's structuralist approach to the ontology of the wave function makes sense (and it seems to me that it does), then this response makes sense as well.

Perhaps when I have more leisure I'll try writing a response detailing what I think are the most plausible responses to your questions, but in the interim I wanted to make sure people know that the Oxford Everettians have thought about this stuff.