Hi antd, nice idea making a X# segments speedrun.
You have probably already seen this but if you havent;
If you want nice tips on how to accomplish things faster I really have to refer to the quickest speedrun I've seen so far http://speeddemosarchive.com/AbesOddysee.html which was posted in 2006. That one is done in 10 segments only and I am confident that you surely can beat that if you time everything 100%.
And about the mines blowing up my tip would be to throw the stone right when the elevator reaches the top while you are standing up, which I think is possible. That way you would get rid of milliseconds stopping one extra time before jumping down.