Dilemma - Past or Present Tense?

I've really never considered writing in present tense, because - well, we naturally tell stories in the past tense, don't we? But, when I started writing my historical narrator's snippets, I found I was writing them down as he said it. OK, he isn't actually speaking directly to me in my head, because hearing voices is scary and weird. But the words seem to fall into the keyboard as if I wasn't involved, I'm just hearing him relate events as they happen for him. The big advantage is he doesn't know what's going to happen, so the events aren't contaminated with the future plot. I could write third person more like that but somehow an overshadowing creeps in.

Anyway, Vincent narrates (mostly) in the present tense, in the 1580s:

The shutters have been left open for air, and I see why when the body is revealed.

The white, swollen thing surely died in the summer, when the waters were warmer, for there is little left of the face, or the hands and feet, perhaps eroded by the sea or eaten by crabs. The swollen flesh make it hard to see whether it is man or woman, as it is naked but for a few rags. It is probably tall enough to be Mistress Agness, and the hair is long, but I have no impression of it being the rector’s demented sister.

‘I know not this person,’ I say, backing away and covering my nose. The stench is vile, and I hack and spit in the air outside. ‘She has only gone into the sea a few weeks since.’

‘There is a widow coming over on the packet, thinks it might be her husband, fell off the quay at Portsmouth last year.’ He bars the door and takes a deep breath of sweet air. ‘Sooner in the ground, the better.’

 Now, I could easily rewrite this as past tense, but I think it loses something in the translation:

The shutters had been left open for air, and I saw why when the body was revealed.

The white, swollen thing had surely died in the summer, when the waters were warmer, for there was little left of the face or the hands and feet, perhaps eroded by the sea or eaten by crabs. The swollen flesh made it hard to see whether it is man or woman, as it was naked but for a few rags. It was probably tall enough to be Mistress Agness, and the hair was long, but I had no impression of it being the rector’s demented sister.

‘I know not this person,’ I said, backing away and covering my nose. The stench was vile, and I hacked and spat in the air outside. ‘She has only gone into the sea a few weeks since.’

‘There is a widow coming over on the packet, thinks it might be her husband, fell off the quay at Portsmouth last year.’ He barred the door and took a deep breath of sweet air. ‘Sooner in the ground, the better.’

Is this better? Worse? Does it matter, as long as I don't mix them up? I'm working on a few longer pieces and would be glad of your opinion! I am mindful of the Philip Pullman article on present tense... 

Oh, and no news. Except one of my poems was shortlisted for the Mslexia poetry prize but it wasn't placed. Still...good competition, and huge field.