I sometimes ride in the drops or hooks, or sometimes with my arms on the tops like OldTryGuy mentioned, just to rest. At least there are some different muscles holding me up, so it feels like resting. I think it's worth spending some time training in those positions to have a ready alternative if nothing else.

IMO it starts and ends with some flexibility and strengthening of the lower back, and getting the neck and shoulders used to it. I look ahead even in the drops with flat back (parallel to the ground) and while at first I was sore (and not that low) that went away in one season if I recall correctly.