I couldn't have chosen a better thing "to have been doing" vs "to do" during a pandemic

[Tony_M]

Source: How a Bee Ruined Jeremy Clarkson's Day | Behind The Scenes Clarkson's Farm | The Grand Tour here. 2:10

Caleb: How did you have to adapt in the pandemic?
Jeremy: It made no difference, as you know. When it first started, I thought, "Oh my god, I'm gonna die," and then thought, "Well, actually, I'm not going to die," because we're marooned on a thousand-acre slab of Oxfordshire, and we're key workers, so we were told we had to keep... nobody clapped us; we had to keep going. I couldn't have chosen a better thing to have been doing during a pandemic, if I'm honest, because we were gainfully employed. We worked every day we were in virtually no danger of catching it because it was nobody around.

What is the function of the perfect continuous infinitive here? What would be the difference between the simple infinitive and the perfect continuous infinitive in this context?

 

[Skrej]

What is the function of the perfect continuous infinitive here?

Here it emphasizes the duration of the past ongoing activity during another past event.

What would be the difference between the simple infinitive and the perfect continuous infinitive in this context?

Effectively none. Perhaps the continuous ties it more to the past, where the simple establishes a more theoretical situation but that's really over-analyzing and unnecessary hair-splinting that makes not one whit of difference to his intended point: they had an ideal job during a bad time.

To that point either version works equally well.