[hopewrites]

i would love to add a bit of Sci-Fi plausibility to my Fantasy setting. to create the world where my story takes place i have destroyed Earth enough to rework it to my stories needs.
the method of destruction i have chosen is Mass Nuclear decimation. takeing the idea that the MAD counter-strike measures would some how be catastrophically domino-ed into effect wiping out most of the population and reducing to rubble all major metropolises.
to be perfectly honest i chose to do this because i am lazy. i dont really want to create a planet from scratch, but i dont want to be tied into remembering where everything is geographically and keeping my ruins accurate. so i chose a method of destruction that i assumed would take some time for Earth to recover from, which would give me time to reshape it to suit my needs.

however i have come up against a plausibility question that i just cant seem to get answered while looking up the after- and side-effects of Nuclear alterations to the face of the planet.

How long would it take the planet to recover?

and by recover, i mean "become a tropical paradise." equatorial desserts, vast tropic regions, smallish temperate regions, no ice caps to speak of.

i figured if i combined nuclear salting of suberban areas with the mass bombing of the metropolises i could get enough soot in the atmosphere for a decent nuclear winter while taking out enough ozone to thoroughly end the ice age we are barely clinging to now. this would also begin the prolog perfectly with the need to save what remains of humanity perfectly clear and unquestionable. so its all set up with the Saviors, the Saved, and the Survivors who make up the racial cast of my story.
but the whole thing is driven by the protagonists quest to gather the myths and legends of the remaining peoples. so i need to know how believed/ disregarded these stories are, as well as how many centuries i have to create them. which means i kind of need some plausible guideline for how long it would take Earth to recover to the point i want for my story from the way i began it.

any advice would be appreciated. i fully expect this work of fiction to take a long time to shape and perfect, especially as i will be working on it around finding a paying job, and then working said job, and then around school in a year or two. but i am so in love with the project and know it will be epically-delicious when ever i do complete it.