Allen points out that there were no 'T55' or 'T58' designations...

Firstly, as background, it's important to remember that the term "T58" was not used at the time. Cooper only invented their "T" number system in 1963, so the T58 was just the V8 Climax prototype to reporters in 1961 and 1962.
He also says this of the Bowmaker-owned F1/2/61:

One clue may be that Parnell had a spare Cooper for the 1963 'Tasman' races two months later. It's not obvious what that was, as Parnell had sold or wrecked all three cars they had taken out to the antipodes in 1962 (F1-1-61 to South Africa. F1-2-61 to Lex Davison and F1-4-61 wrecked by Salvadori). Could it be they took the T58 as their spare and that was the car raced by Jim Palmer? Photographs of Palmer's would be really useful.
So that car was already with Davison in '62.