One simple solution is to put a layer of plywood on the slide, extending out over the [now] flexible extension. Basically stiffen it up to carry the vinyl (or whatever you choose). You will raise the slide floor 3/8" or 1/2" that way and most do not find the slight lip to be a problem. Use a molding of some sort to cap the edge, so your feet do not scuff the edges of the tiles or planks and pull them up. Stair nose works nicely, but you can simply tack a flat molding (e.g. screen molding) to the plywood edge if you like. Whatever aesthetics suit you.
2004 American Tradition; 2013 Buick Verano
Homebase in the Ocala Nat'l Forest near Ocala, FL