Any variation in the substrate will telegraph through your vynil floor. Sustrate needs to be flat and smooth. You can skim the tile and hardwood as long as it is not loose.

Even nail pops telegraph through lvp (ask me how I know) the substrate has to be perfectly smooth.

Maybe look at the 'new' laminate. Reformulated to be waterproof. You need something with a strong locking system and less flex. For lvp Modine by Flooret could be considered. It's direct sales. They have recently added laminate. Call them. 800-700-8122. They like to talk flooring. They know their product. Arista Waterproof Laminate - Flooret

All the existing flooring must be removed back to the subfloor. Then it needs to be flattened. Only then can you install new flooring.