Phizzy....IMO the generally ambiguous references to the death, even the ambiguous terminology, all contribute to the theological development of the story.
First off there was no specific noun or verb that differentiated the Roman (or earlier) use of a two or more piece implement for execution (or postmortem public suspension). Therefore, insisting that the words used have any particular narrow definition is bringing something to the text. (unless the context makes clear what the author is describing.) All relevant terminology appears to have had usage beyond the simple etymology of the words. Such is typical of language.
As Phizzy pointed out, there is a larger question in play. Given the pre-Christian symbolism of public execution and suspension (on tree, pole) we have to consider whether the earliest pre-Gospel Christians had the Roman execution methods in mind at all. For example, Doherty's thesis concludes that at the foundation of Christianity is a passion play in the spirit realm that was euhemerized in the Gospel story through use of OT typology and the contemporary Roman domination of Israel. Without further expansion on this thought, I'll suggest that this is consistent with the issue under discussion. The NT has the concept of 'suspension' (with theological implications) foremost, not the particular shape of the implement, though in some contexts it seems clear they had a cross in mind.