It IS possible to work the problem from Diana's "perspective". You can indeed ask the question: "At each instant of Diana's life during the trip, what does she conclude about Artemis' current age at that instant?". You can get that answer (for each instant "t" in Diana's life) by using the "co-moving inertial frame" at that instant. The Lorentz equations can be used to relate that "co-moving inertial frame" and Artemis' inertial frame ... i.e., the Lorentz equations can tell you what Artemis' current age is when Diana's age is "t", ACCORDING TO DIANA. That capitalized phrase is needed, because Artemis will NOT agree ... his conclusions about the relationship between their ages during (most of) the trip are quite different from Diana's conclusions. The whole process for carrying out the above procedure is well described in the webpage
The short answer is that, according to Diana, Artemis ages slowly during Diana's constant-speed outbound and inbound portions of her trip, but during her accelerated turnaround, Artemis ages VERY quickly. And the TOTAL of those three components of Artemis' aging is such that Artemis' and Diana's "perspectives" both agree at the end of the trip (but they generally disagree during the trip).
I know nothing about the CADO reference frame methodology. But your explanation is spot on. For some observers (accelerating ones) an inertially moving clock runs FASTER. That is a consequence of Special Relativity.
by Richard A Mould
Chapter 8 "Uniform Acceleration"