How to cut a "nice" hole in an engineered wood floor

Some sort of brass port hole, could make a feature?

Yes, that was my immediate thought. If rectangular, similar kind of brass trim.

How much space is underneath the floor? - can't the hatch go under the stairs or in some other inconspicuous place?

If its a floating floor that isn't nailed down you could just take it up strip by strip.

There's various access-hole systems out there. I haven't tried any of them, but here's an example:

I'll go with the brass idea. Cut out the panel (Fein type tool would do this without issue but there are other ways).

Easy: brass angle round the hole and the hatch - screwed or glued at the edges. Mitre the corners.

Harder: same thing but rebate both so the brass is flush. If you were really lucky, you might be able to get brass U section round the hatch which would help hold it togther if it spanned more than one strip.

Assuming it's strips with a plank-like finish I'd consider using a multitool to make very narrow cuts across a strip and to cut the tongues locking the cut section of strip to its neighbours so you can remove a small rectangle.

There are various ways I might think of arranging to hold the cut section in place when you re-fit it.

If its real floor boards, cut a single section of board out and use something neater than featherspitter to take tongue off, support board back in place with dwangs put in between joists.

If its some sort of engineered finish, floor box lid, these people are at the top end

Thinking a bit more , and looking at this pic

Cheers Adam