Pause the original keyword, don't delete it. If things go poorly for the keyword in it's new location, you'll need to reactivate the original keyword with it's original history, which you can do if it's paused.
I suggest in the new ad groups, run the same ad the keyword was originally paired with along with a new, more targeted ad. As per usual, keep the one which performs better. Keyword QS is closely tied with ad text, so a whole new ad may be a disadvantage.
Pull your QS in advance of making changes, so you can run a post-opt comparison and roll back anything that didn't improve.
Quality score is calculated on several levels, but only visible at the keyword level, and only as a summary:
1. Account/Domain - the history of performance (CTR) for your domain.
2. Google Search - history of performance on Google. Both Account & Keyword level.
3. Search Partner - history of performance on search partner network. Both Account & Keyword level.
4. Content Network - history of performance on content partner network. Both Account & Group level.
All of the above are calculated per geography as well, which you can only see if the campaigns are set up per country.
I also suggest either not changing your bid for the "moved" keyword. Or even increase bids at the start, then ease them back down.
If you do migrate everything over to a new structure, keep content and search separate, and leave the content network running on the old campaigns. Maintaining performance while reorganizing is a lot harder for content than it is for search.
The faster you get clicks, the faster your QS will change. Most importantly, CTR is king so it's important to make sure that is high from the start.
Tread lightly and good luck!