Rebirth, is the continuation of anatta.
How can this be when the suttas say the realisation of anatta leads to the ending of birth?
Seeing thus, the well-instructed disciple of the noble ones grows disenchanted with form, disenchanted with feeling, disenchanted with
perception, disenchanted with fabrications, disenchanted with
consciousness. Disenchanted, he becomes dispassionate. Through
dispassion, he is fully released. With full release, there is the
knowledge, 'Fully released.' He discerns that 'Birth is ended, the
holy life fulfilled, the task done. There is nothing further for this
world.'
SN 22.59
..
no Self can be said to transmigrate
This sounds like the heresy of Buddhaghosa about the 12-fold voidness. If rebirth was not-self, there would be no incentive to do good kamma because the results of kamma would be impersonal. Also, if no-self transmigrated, there would be not need to take refuge in impermanence. This heresy of Buddhaghosa destroys all Dhamma, both mundane & supramundane Dhamma. This Buddhaghosa heresy destroys incentive to do good personal kamma & destroys the Three Characteristics. It destroys morality & destroys liberation.
- only the statement that 'dependently originated phenomena (any conditioned and posited self) cannot have permanent properties', can
be accurately put forward. Is nibbana therefore, still the
continuation of anatta, but without dependent origination?
Anatta is unrelated to dependent origination, which is why the Buddha did not teach dependent origination in SN 22.59, which resulted in the first five arahants. All things are anatta, regardless of dependent origination.
Can it be said that dependent origination - impermanent and unsatisfactory - is distinct, or at least not identical, to anatta?
Yes. Absolutely. The Dhamma (Dhp 279) says "sabbe dhamma anatta ti" - all things, be they permanent or impermanent, be they conditioned or unconditioned, are anatta.