After a lot of hand-wringing, I think the TC break thing (in ProRes, anyway) is due to a 10-bit digitizer conflict with the Kona card. Thanks for all your responses, by the way.
I messed around with the capture preset and changed the Digitizer field in ProResHQ to Kona 8-bit, and that seemed to work at 1080i 29.97 (the Digitizer field was defaulted to 10bit at both ProRes and ProResHQ.)
and for David, I would check on your J-H3 to see if it is mistakenly on the pull-down setting? It will read 23.98PD if it is, but for DVCProHD it should be 23.98psf.