Caveat .. didn't fly the NG only the Classic so my comments have to be generic ..
This is one of those conundrums where you might very well be "damned if you do and damned if you don't" . The correct answer is determined retrospectively by the outcome on the day .... and the Judge at the Enquiry ... if the outcome was less than fortunate on the day ..
As with so many things we discuss in this sandpit ... it all depends.... Certification tends toward the black and white (as it must do ... to be achieveable and repeatable) while the real world is a murky mixture of all shade of greys ..
Things which concern me include ..
(a) the chart accel stop data is based on a fuel cut at Vef .. ie one winding down rapidly and the resulting speed overshoot being contingent upon that very significant thrust reduction
(b) fire warning leaves you with two engines and a significantly higher acceleration (and speed over run .. 5-15kt might be a reasonable ball park figure) while you are going through the reconfiguration from go to stop mode ... ie if the takeoff is seriously accel stop limiting you are absolutely guaranteeing an over run if you stop ...
(c) how far below V1 is "just below V1" when the event manifests itself ? .. considering the particular Certification Basis for the aircraft ...
(d) how long is it since the far end has been cleaned of rubber deposits ? what is the over run like ? what is the crosswind ?
(e) if the runway is not accel stop limiting and has a comfortable margin (bit rubbery until the margin is large) .. then stop
(f) if the runway is accel stop limiting and the over run is nasty .. I'd keep going on the basis that the historicals favour that option on a risk management basis
(g) let's not argue about reverse thrust .. in a real serious situation the maximum effort deceleration is sufficiently high (those who have felt the effect of nosewheel brakes on the 727 will understand what I mean) that the practical effect of reverse is comparatively small in the overall scheme of things.
Of course, we could come up with a few more considerations with a modicum of thought .. but, whichever way you look at it ... it's not a nice place to be.
you have about 3 to 4 minutes to destruction .. which is why some of us push students on endorsements with a contrived minimum time circuit exercise .. engine or cabin fire .. same sort of scenario and concerns ..
.. some days one really should have stayed in bed .. for instance I have a friend who has driven a wheelchair for many years ... having stood in for another colleague on a particular test flight ... same sort of consideration at play .. all one can reasonably do is operate conservatively .. load the dice reasonably to your benefit ... and hope that Lady Luck, on those occasions that she is irritated, visits other people instead of oneself ...