Can I add another option to the mix - pushing exposure in post (Lightroom or Photoshop)?
Essentially, using high ISO is an amplification process that boosts your signal, but also boosts noise. You can do the same amplification in post, where you have more control of which parts of the image you boost.
I use a Leica M9, which has notoriously weak high ISO performance above 800. Some kind soul (I can chase up the reference if needed) has compared using high ISO vs adjustment in post, and concluded that, for the M9, beyond 640 you get less noise by boosting in post than increasing ISO. In other words, the S/N ratio increases excessively above 640 - boosting the 640 image allows you to exploit the lower S/N ratio. Other cameras would have different thresholds.
In my own trials I find this works as long as (a) I do not push it more than 2 stops in post, equivalent to using ISO 2500 instead of the actual ISO 640, and (b) the images have reasonable contrast with most of the interest in the lighter parts, so the noisier shadows can be held back.
A downside of this approach for amateurs who chimp (professionals don't chimp, right?
) is that the image on the screen is too dark to review properly.