First, the problem is not peculiar to any one Type and bleeds off to squeeze a bit more goes without saying ....
Second, it is not a case of "being OK" .. either the sums justify the RTOW and associated speed schedule ... or they don't.
"Winging it" is never easy to defend in court after the accident ... and be VERY sure that you (the crew) will be very much on your own in this case.
If you are obstacle-limited and seeking a little additional weight, it becomes a matter of redoing the sums. Depending on where the limiting obstacle is located, an overspeed (improved climb performance) schedule may (if the obstacle is distant - say fourth segment) or may not (if the obstacle is close - first or second segment) help. It is all a case of matching a longer takeoff distance against better climb performance (all segments, not just second) and seeing where the obstacle is in relation to the reworked net flight path ... some you win ... some you don't ...
Kilo .. if you redo the sums for an overspeed schedule, the previous limiting weights cease to be valid .. each separate speed schedule calculation set stands alone. If the problem is obstacle limits, then chances are that you will be looking for better than WAT-limiting climb performance. Please be wary of concentrating solely on second segment .. each segment has to be looked at to meet the required calculation set.
This all presumes, of course, that no other required case becomes limiting and spoils the overspeed gameplan.