Re the 747 particularly:
Look in the AFM to see the all engine and three engine takeoff distance and you will see that the all engine case is limiting. This is because the all engine net figures are reduced by 15 percent, while the three engine case is not. The three engine performance degradation is not as much as 15 percent, since it only applies to the continued takeoff beyond V1.
Many inexperienced pilots will be amazed at how close the end of the runway appears to be when the airplane lifts off, but this is immaterial; the time to check the runway remaining is when the airplane reaches V1. The stop case is limiting on all engines. Should the decision be made to reject at V1 then the three engine case benefits from the all engine 15 percent margin also, so in practice the crew have the advantage of reverse as well as the all engine margin and unless there is a brake problem or runway contamination, a stop should not present a problem. Hot brakes, sure. See the Boeing performance tapes.
If the PF waits until he hears the "VR" call before starting the rotation then a lot of runway will disappear before the airplane flies. Starting to reduce the weight on the nosewheel prior to VR will allow a lift off right on or just prior to V2 and make the picture look better. But there is enough performance available for the pilot to pull the airplane off the ground instantly if he feels it necessary. Crossing the end of the runway below 35 feet is not a problem, so long as there is a clearway or stopway.
Boeing recommends the use of symmetrical reverse, but personally I reckon that if a 777 can use reverse on one side a 747 should have no problem with three engines in reverse on takeoff abort or landing. At least initially, but it is my opinion only.
At heavy weights and an aft cg it is not a good idea to do a full power runup prior to takeoff, despite what some company manuals might tell you.
When calculating V1 for contaminated runways, using the V1 for the max weight for those conditions regardless of actual weight and applying the corrections to the higher V1 (then use the lower of the dry V1 or the max V1 with corrections) gives a safer solution. In fact whenever the weight is less than maximum for the runway and conditions, the true V1 is that for the max weight, which means that V1 can be increased to VR in most cases. But do not do this unless you are qualified to calculate these numbers. Knowing that you have a pad should take away some of those jitters and allow you to carry out a reject in a deliberate and positive manner rather than rush it, thinking that you are running out of runway.
Boeing (and the FAA) do not consider the failure of two engines on the same side during takeoff, and it is statistically so remote a possiblility that it can be ignored. But it is an interesting simulator exercise. The Vmca for two engines is around 186 knots (anyone who has a better figure?). This is above the V2 for all engines at max TOW. Although it is not likely to be a real world problem, it is a good idea to use (company permitting) F10 to reduce the drag and maybe allow maintenance of Vmca. If the speed drops below Vmca then thrust will have to be reduced and at more than light weights this will give a negative gradient of climb. The latest Boeing Training Manual shows that tail clearance is not reduced by much if F10 is used, contrary to what had been published before.
Training in performance nowadays is pretty poor. Then again, most training nowadays is the same, with the goal being to provide the pilots with the minimum amount of knowledge needed to do the job. A good pilot will realise this and make an attempt to learn something new every day.