Permalinks Aaaargh!

I have built a site – it’s pretty huge see it here.

I built it using ugly permalinks and now need to migrate it to pretty ones (%post-name%), the problem is that the site is full of readmore buttons etc all linked to the relevant sub pages and pretty permalinks seems to break these button links.

I have tried a number of plugins (yoast SEO & Custom Permalinks) to no avail. I sam “Search and Replace” being suggested, but don’t understand how I could use it to acheive what I want.

Is there a solution to this, there are literally hundreds of internal links so changing them one by one would be a nightmare.