Don't take chances. Once you've set up a 410 or a 301, leave it there forever. The day after you delete a 301/410, google will dig up its Forgotten URLs list and request the page.
At the same time, you should test the new system thoroughly to make sure any bogus URLs result in a 404. It doesn't matter what the (human) user sees, so long as a 404 response is returned. It is better to find this out ahead of time by experiment than to find out after-the-fact that search engines have been requesting and indexing nonexistent URLs. See if you can tweak your CMS so that any content returned with a 404 response includes a <noindex> tag. (This may not be mechanically possible.)
It isn't clear from your post whether the new site will be at a new hostname, or simply a major redesign.
As it happens, I moved recently. Along with the redirects, I did the following. All of them happen before the generic old-to-new redirect.
--all existing 410s continue to be served at the old hostname --all existing 301 redirects remain in place at the old hostname, changing only the hostname of the target --any changes made after the move are duplicated in htaccess, with matching redirects issued from both old and new hostnames. (I mean, of course, for URLs that existed at the old name and would otherwise be subject to generic redirect.)