Easy way to reconfigure all our categories?

I want to redo our categories, as over time we have added more and more, and it's all got a bit messy.
We have over 3000 products, and around 20 categories now.

I thought Easy Populate would help, but it turns out to recategorise, I would need every single product to have a model number.
However only about 60% of our products do (all those entered before I used Easy Populate don't)

So I guess the first question is..
Is there an easy way to add a unique model number to every product that doesn't currently have one?
Or would it work to just reassign model numbers to ALL products sequencially, overwriting what ever model number they have right now?

Otherwise, any other suggestions for handling this?

I did used to use a self written vbscript which connected ot the web server and recategorised all products based on a local folder structure, but it's not the best way as I lose the master category for each product as it erases all categories and reassigns them from scratch each time.

If needed, our website is www.funkimunkibadges.co.uk

Thanks!