Here's an idea, instead of separately tracking the number of "resets" we just add those bits on to the left hand side of the measurement. We could call it... having more bits in the ADC. Expose for the highlights and then pull more detail out of the shadows with your extra bits of ADC precision.
There are not 1 million ADC units in a 1-megapixel camera, there's a few ADCs (a Canon 7D has 2 image processors with 4 ADCs each) that are iterated across the CCD sites to progressively read them out. To make this new sensor, you need to cram 50 million sets (50mp is state of the art) of voltage comparator/charge reset/digital counter circuits onto the CCD, and for N bits of rollover accuracy they need to be able to trigger, erase the charge, and resume exposure at least N times during the exposure time E (which is say 1/500th of a second, since they're complaining about movement during multiple HDR exposures). Practically speaking the trigger/operation/resume period must be significantly less than E/N since I see no way to retain the exposure during the period when the charge well is being drained to zero. If this time is non-trivial, that translates to losing the fine bits of your ADC accuracy.
In their image they compare a 13-stop exposure (the current state of the art) to an 8-stop exposure (state of the art in 1900). So assuming they didn't just pull a photoshop out of their ass, they are overall claiming a 5 stop increase from state of the art. That's 5 extra bits of recovery (1 stop is double the range, i.e. an extra bit), so they think they can trigger the reset circuit 5 times during an exposure. That implies this circuit must have a minimum cycle time of 1/2500th of a second (practically speaking a lot less to give time for the actual exposure). With this math I'm also assuming that the comparator is perfect and doesn't lose any accuracy - variance in trigger threshold or trigger time translates to losing some of your accuracy again. They also need to generate little enough waste heat to avoid hot pixels (this is a major reason the ADC is on the image processor rather than the CCD), and you need 50 million sets of these on the CCD.
If you can do it then go for it. It's a nice idea on paper but I think there's a lot of physical obstacles to overcome. If it were that easy someone would have done it already. It's especially difficult given that reading out the sensor is destructive - measuring it wipes the charge, so I'm not sure how any of this would work at all given that.
Now what would actually be interesting is to apply the image-processing techniques to dual-DR imaging, as they mention in their "related works" section. The open-source Magic Lantern firmware for Canon DSLRs allows you to scan alternating rows at different ISOs, so effectively you can capture a lot more dynamic range at the expense of your vertical resolution. It's all volunteers and they probably haven't applied all the fancy image-processing magic with the convolutions and the hippity-hop rap music. How about reconstructing those overexposed lines instead? Or working on some of the sensors with physical implementations of dual-DR?