I've had to do this a few times and to my knowledge there isn't an easy way to switch the template of a landing page in the way you described. I believe you have to clone the landing page and select the new template when you create the new version of the landing page.
To keep the same URL, you have to edit the old landing page URL (selecting the "throw away old URL" option) then update the URL of the new page with the desired address.
If there is a faster way to do this, I would love to know!
This process could be prohibitively time-consuming for many landing pages, so editing the old template and re-approving your landing pages, as described by Justin above, would be the most efficient way to proceed.