It's a cool thought experiment but if I could offer my two cents, I don't think a colony ship like this would ever be feasible.

The main issue is the quantity of ionizing radiation in deep space. Over long periods of time, you'll have enough gamma and cosmic rays that will completely destroy any sort of information storage that you attempt to have. This means both biologically (DNA) and computationally (any form of digital storage).

To solve this problem, you'd need either a passive defense system or an active defense system.

A passive defense system against gamma/cosmic rays is basically just being on a planet. You wouldn't need special storage while residing on a planet.

An active defense system would require an incredible quantity of energy. You'd have to constantly check the DNA/digital storage and make sure that none of it was corrupted. You'd need sophisticated repair and backups for both of these systems. However, the problem with active defense is that the quantity of energy that you can get in deep space is very small, you can't really use solar as you're too far from the sun. The only option is to bring enough energy with you to survive a trip that could take centuries. I don't find this very feasible.