"l
et's say 4 stops" (...) "
brightest part to be in zone V and the darkest to zone II in the print" the way I count: II+4=VI, but anyway...
A print spanning zones II to V, starting at dark gray (no black) and maxing at middle gray, will look..., well, it's up to you
Is it better to expose the negative in that way or I should expose say zone IV to VII and just underexpose the print?
If the limited brightness range of the subject allows it, I would indeed expose a little more: zones (III-VI) or (IV-VII) as you suggest. The neg wil be more dense (and have better separation in the shadows), you will need to expose
more, not less under the enlarger.
Is it better to do a little longer development to stretch out the zones then print on higher contrast
If you develop the negative longer, it will have higher contrast; to acheive (more or less) the same print you need a paper with
less contrast, not more. And indeed with such a low brightness range subject, I would develop the negative to a higher contrast (but then not increase the exposure as mentioned above); a print spanning zones II-V will not look like the example image that you posted; darker, dull.