Given the strong demand for their current products, there is no incentive to rush new products out. Nvidia has less incentive since they are the market leader. This will give them PLENTY of time to be able to work on their processes and yields on engineering sample products to make the transition much smoother. I would expect that NVidia will do as they are currently doing, pushing their newest architecture in limited volumes at the very top end of the market (engineering and rendering and specialty products) to iron out any production issues that they may have. They can afford this because almost their entire product stack is selling at volume at or above MSRP. When they get yields to target levels, and drivers where they want them to be, they'll do the switch and fill the channels, winding down old products as they stop selling at MSRP.
AMD doesn't have the technical lead, so they are likely constrained by their R&D as well as their production limitations. Given how low their past volumes were, their production capabilities are likely tuned to lower volumes than Nvidia. This makes capacity increases harder and more expensive for them. They do have a significant chance to catch up a bit with R&D here as Nvidia has been conservative with their Volta rollout, though, given how big the gap is, its likely that they won't be able to gain any significant ground.
The true kicker here is that, hashing algorithms are quite well defined. It is easy for both AMD and NVIDIA to profile how the various hashing algorithms behave with their GPUs and make very minor tweaks to the bios or micro-code of a portion of their cards that will make them perform significantly worse for hashing while not adversley harming their gaming performance. This would allow them to sell "premium" mining cards while still selling "gaming" cards at reasonable MSRPs. This would also allow them more control over channel volume. They could sell gaming specific cards at levels that make sense for the market, and then push as many mining card out the door at a premium price as the market will bear. This would be no different than how both AMD and NVidia have made Quadro/FirePro cards for the professional market as separate products based on the very same chips in many cases from the gaming cards in the past. Yes, it will harm their resale values, but, if configured to be optimized for hashing from the factory, the extra performance would be worth it.