"I think he considered the "anatta vs atta" issue to be far more significant than talk of multiple lives."
that's the real point.
"I" exist because an ignorance of patticasamuppada. "I" will die due the same ignorance. But finally there is not an "I" able to born and die. Then, What's the thing able to be born and die?
We can say: "there is 4 o'clock". Why?. Because before was "3 o'clock" and we infere how later it will be 5 o'clock. However, the hour in itself didn't exist. Hours appears like conditioned things. Because nobody is able to perceive one hour. We need mental images and third references to claim the existence of time because the time cannot be claimed without references.
My past live and my future live only exists while I'm conceiving an actual present thing called "my live". But in fact there is not "me" or "my". Without references finally there is only no-time, the actual present and the live to be lived.
Although to make useful Buddhaghosa, there is also the case in where somebody say "3 and 5 o'clock didn't exist, it only exist the 4 o'clock and this is the only existent hour. There are not more hours". I think this is a worse non-sense. Because if we admit the 4 o'clock for sure we need 3 and 5. Here it can be an utility for the 3 times schema. Sometimes it can work like a provisional station to disentangle the ignorance of the only existence of the 4 o'clock.
But when we need to talk in Dhamma terms and regarding the final meanings in dhamma, then one start knowing that there is not "me" and "my". Therefore there is not rebirth of the 3,4,5 but there is only an explanation of the arising of the time. This arising cannot be explained in primordial substances called hours, seconds, miliseconds or any other measure. The explanation is about how the time is created. If we create any substance maked of time (hours, minutes...) to explain how the time arises, then we fall in eternalism. At least I believe it is the sense in Buddhadhasa when rejecting rebirth in those terms.
In the conventional side, probably Buddhadhasa claimed rebirth by the same logic he used in the distinction of dhamma language. But sure in Thailand his efforts to teach patticasmuppada were more successful avoiding this point.