The way we get taught, after you pass through LDP there is no choice - you must land. This is due to not having the performance after LDP to carry out a single engine go-around without coming below 35ft above the ground (class 1 go-around requirements). Similarly with the TDP on a class 1 departure, if anything happens before TDP we have no choice, and must reject. We have some discrepancy wether to continue or reject after TDP, but the assumption unless otherwise briefed would be that you would continue. If we're departing class 2 then there is no specific TDP, only a stated VToss. The pilot just makes a judgement call when he thinks on that particular day he would continue if anything went wrong. With class 1 the performance is guaranteed below 500 feet, class 2 isn't.
The more interesting scenario would be approaching a rig before passing the commited point (no LDP as not flying class 1 off-shore). Would you land single engine on a rig, with no gaurantee of landing performance, or would you go-around and fly back into the air with an engine on fire?
Interesting to think about these cases, and hopefully that's all any of us will ever do!
