Shimano Ultegra chaninrings on Truvativ Elita Tandem crank I'm attempting to replace the chainrings on my Cannondale Road tandem. The crankset is a Truvativ Elita Tandem (52-39 10 speed big/middle ring). The new rings are Shimano 6603 52-39 rings.

I swapped out the rings without issue. I've also replaced the cassette and drive chain.

The chain runs fine in the big ring.

The problem shows up with the chain on the middle ring and on the three smallest cogs of the cassette. In those gears, the chain skips frequently. It appears to try to jump up to the big ring, then falls back down, a couple of teeth back on the middle ring. It is skipping more than once per chain cycle, which I think rules out a problem with the chain.

Watching the chain closely it appears what is happening is that the chain is catching on the little shifting helper nubs on the inside of the big chainring.

It is not the derailleur causing the chain to shift. I've made sure the derailleur is not touching the chain. The same thing also happens on the bottom of the chainring if I backpedal.

Is there any reasons these rings would be a problem on this crankset? Any other things to try?
I can't say for sure if the chainrings work on that crank in your particular configuration. It sounds like they should.
Keep in mind that road triples are inherently troublesome (though some might disagree with me) and require a little more mucking with to get adjusted. If your front shifter doesn't have trim/half shifts between full shifts, you may need to let out the cable on your front derailleur a little and actually let the chain drag slightly against the cage when in those extreme gears on the cassette. This will keep the chain off of the shifting pins of the big chain ring. Not real awesome but it might be the best you can get away with on your current setup.
It also sounds like your chainline is not optimal. Are there any spacers between the bottom bracket shell and the outboard bearing cups? If so, you may need to move one to the drive side. If not, don't add them.
Worst case you may need to go back to Truvativ rings. Hard to say for sure as it's always difficult to diagnose bikes over the internet.