Here is my approach, followed by my opinion on shroud tension during storage.



Secure the back end of the main halyard so that it can not escape; either use a stopper knot/stopper ball, or tie it off to something.



With the main block and tackle on the boom and traveler, raise the boom untill the block and tackle are fully extended. Attach the halyard to the outhaul so it suspends the boom at this height.



Slide the traveller all the way out to one side. Sheet in hard. Now the shroud on that side of the boat can be adjusted.



Keep this tension on the rig when storing in a mast up situation. If practical, set the boom and traveller and main sheet up just as I described earlier and put some tension on it. The tension in the halyard and on the boom will force the mast to rotate and hold it there so that it won't oscillate in the wind.



A tensioned rig will move around a lot less than a loose one. The movement is the worst wear on rigging. Think of bending wire back and forth, thousands of times. It weakens it.



Keeping the whole system loaded will avoid most movement and therefore minmize wear and tear.



I don't leave my main sheet on the boat but rather I tie the boom to the traveller with the remaining end of the halyard. Any piece of line will do.