I added some angle iron to mine today. Only issue we had was that 2 of the screws(one on each side) would not thread back in and hold. The front 2 screws we could not remove at all. The top of the screw was apparently spinning and they are under the metal.
The back screw on the left would not bite. We removed it and the screw was rusted bad. I cleaned the grooves and added a bunch of toothpics in the hole. Put the screw back in and it is holding. There is a slight hump in the linoleum but it is livable. I had never done the toothpic trick but the father in law showed it to me.
The step is super solid now. We added 2 pieces of angle iron - one on each side. It goes from the front of the step to the beam(approx 13.25" long) When you step on the step, it goes no where now
Unfortunately, I am positive that there is some floor damage. That might be a later project though. Thanks for posting a possible solution above!