The inertial observer in the centre of the carousel measures those torus segments when they are stationary.
Then, after a million years of a small acceleration of the torus and NOT the central observer, the observer should see segments contracted.
Right?
During the million years of small acceleration, the torus will have to stretch (i.e. each atom's distance from its neighbours, as measured in its own instantaneous inertial frame will increase) and/or break.
Specifying that you do it very slowly doesn't change anything -- suppose you and I are holding the two ends of a rope on the Arctic Circle, and we go south to the Equator each along a meridian; in order for us to do that, the rope will have to stretch or break even if we walk one millimetre per century.
As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.