Heavy landings question
I don't see the energy involved in landing a large aircraft being substantially different from landing a fast aircraft, other than having relatively less specific thrust, and this needing longer to add enough energy to climb away instead.
"Stabilized" to my mind means having steadily declining potential energy and constant kinetic energy: airspeed is steady in gust-free air; rate of descent is steady. The kinetic energy you carry to the ground is then the energy that goes into the air behind the spoilers and alongside the reverse-thrusting engines, and into the brakes. If this "stable" condition isn't met by 1000-2000 feet above the ground, leaving a minimum amount of things to do and avoiding excessive workload near the ground, then you go around and try again.
I'm not sure why your heavy aircraft leaves its steady progress to the ground? Is it a change in wind, or to the degree of a microburst? A change in thrust or drag, or setting up a dutch roll? If none of these things are a big change, and can be quickly countered by the controls and throttles, then the energy is about the same, you're still "stable" in terms of energy, and you should still be safe to land. If you choose to add energy and go around, you need add only a little - just enough per second to overcome the sink rate.
Even as the wheels touch, you're still flying. A fraction of 1% of the energy of the aircraft is sapped away to spin the wheels up, leading to a change by a half of that amount in groundspeed, but you're still almost flying, and still have the whole length of the runway to add power and go around. At that point, if you're happy to decide to brake instead, all the kinetic energy is safely dumped into the wheels and the airflow behind, and you can drive off safely.