Can his original testimony be even referred to in the new cross-examination?
Or is that rendered inadmissible due to the whole original trial being a nullity?
No. It’s rendered inadmissible because it is hearsay - a statement made by the witness outside this trial. Unless there is some exemption to the hearsay rule (e.g. because it contained admissions or a confession) it’s inadmissible.
Does he effectively admit committing perjury by claiming he is saying the truth now, inference being that he was lying under oath previously?
Perjury is not just swearing a falsehood. To be perjury, the falsehood must be material and must be a deliberate lie (an untruth spoken knowing that it is untrue).
Like most other crimes in the common law system, to be convicted of perjury one must have had the intention (mens rea) to commit the act and to have actually committed the act (actus reus). Further, statements that are facts cannot be considered perjury, even if they might arguably constitute an omission, and it is not perjury to lie about matters that are immaterial to the legal proceeding. Statements that entail an interpretation of fact are not perjury because people often draw inaccurate conclusions unwittingly or make honest mistakes without the intent to deceive. Individuals may have honest but mistaken beliefs about certain facts or their recollection may be inaccurate, or may have a different perception of what is the accurate way to state the truth. In some jurisdictions, no crime has occurred when a false statement is (intentionally or unintentionally) made while under oath or subject to penalty. Instead, criminal culpability attaches only at the instant the declarant falsely asserts the truth of statements (made or to be made) that are material to the outcome of the proceeding.
To prove perjury, it is not enough to show that the statements are inconsistent. The prosecution must show they were material to the trial (i.e. they must be about guilt or innocence) and the defendant knew they were lying at the time they were spoken. A defendant who has “changed their mind” over the passage of time cannot be said to be lying in either trial. They believed X then, now they believe Y - that’s not perjury even if X or Y or both are untrue. One of them being false is a necessary but not sufficient condition for perjury.