Now that extended sitting is thought inadvisable, would it be better to lie down periodically, to minimize the sitting time?

How about walking: I am not sure what you mean by extended sitting time. To stay healthy walking in between activities like watching tv is beneficial for health.

Sitting is Bad: I really believe that the amount one sits is just another indication of a sedentary lifestyle aka "couch potato" laying down is unlikely to produce an improvement. Getting up and walking up/down some stairs or around the block or getting on a treadmill is more adviseable.

Stand up: Ot would seem better to stand up, stretch, move one's arms and legs. You don't want a problem with deep vein thrombosis, blood clots in the legs.