How can we do to have a contingency procedures available for a runway in a couple of hours ?
That is the problem over which all reputable operators concern themselves. There is no easy way around the problem and all solutions cost resources both in terms of dollars and time.
There are various organisations around who will do the work for a dollar (or many) or you can train up internal resources to do the work. The difficulty is not with the actual calculations .. they are comparatively straightforward and can be done either manually or via computer. The latter requires either the OEM performance package or the development either of lookup tables or regression equations to fit the AFM data).
The routine effort has to be directed towards getting adequate obstacle data. Generally, and especially if you don't need the very last kilo, you can run up a one off calculation without too much delay .. once you have decided that your obstacle profile is of sufficient accuracy.
Can we use the SID single engine ?
Of course, provided that you match the actual obstruction profile to your aircraft's capability and accept whatever RTOWs fall out of the sausage machine. A side issue relates to imposing an increased level of precision on turning points ..