Crossover chain wobble.
 

I have had the Tandem for about 5 years now and I have to admit that I am a mechanic. One of the problems I had when I got the Tandem was the crossover chain. It had a tight spot and a loose spot on the chain. Took a lot of adjustment but By carefull adjustment I got it so that the tight and loose spot on the chain virtually disappeared. The cranks fitted to the bike were Sugino and the rings were only a cheap steel form.
This year they were up for replacement and I decided to go for a good quality ring. Choice in the UK may not be as good as the rest of you But One good Ring manufacturer is Middleburn. Just aswell as besides the shimano stock rings- this was the only branded name my LBS stocked. Fitted them and no adjustment necessary to get the tight/loose spot out. And I mean no adjustment. Checking the Tandem over yesterday and adjusted out the concentric to take out a bit of play in the chain. There is absolutely no difference in tension on the chain- wherever the cranks are in their rotation.

I may be lucky in having a set of cranks that are true after around 5,000 miles offroad, but those rings are not luck- They are just well engineered.

Middleburn may not be well known in the US, but they do make some fine componentry. Most chainrings are not 100% round, as you have found out.

some chainrings are manufactured oval to gear down for the awkward apex of the crank rotation and gear up for the easy midstroke, the old chainrings probably wern't designed for the timing chain on a tandem and that you were just lucky the middleburn ones wern't manufactured with this oval technology.

middleburn is ace though, they'll last for years, the quality of the alloys and the machining is.. mega