You could probably get it off the ground a lot faster if you lost the self-replicating requirement. (Self-replication / self organization is super cool and a research field of mine, but still a ways away from production).
Just make a lot of them to start with and clean them up when/if they're done. Or make them biodegradable.
The swarm is self-replicating, not each individual bot. (Have you ever read Alan Dean Foster's "Sentenced to Prism" (sic)?) The system is more like an ant nest.
Self-replication is required to be able to make a lot of them in a reasonable amount of time.
Once the bulk of the plastic has been sequestered excess robots will be glued together to make a floating island.
There's no "done" state until/unless we stop throwing non-biodegradable matter into the Oceans.
Just make a lot of them to start with and clean them up when/if they're done. Or make them biodegradable.