As a quick follow-up to my original post:

3rd World card converted to WE on 12-22 (did secure message to Citi on 12-30-15 - confirmed WE and card will be mailed soon). I noticed name change in myciti.com around Christmas time with no email or notice.

Datapoint - Citi system shows all WEs for me, yet new World Elite card not mailed yet...and thus not activated.

Applied today using link 14 (link 13 did not work - 404--oops notice on citi.com) and instantly approved for new World card #4.

So it looks like you can start cycle again without receiving physical new WE card since it can take some time for Citi to actually mail it after converting you (weeks).