Canadian practice was something like:
Inside Stephensons – remove the straps, so that they get lost for preservation; (as per the E10-A in Morrisburg, ON)
Remove the connecting rods, keep the coupling rods on – but that means removing the return crank.
Both CPR and CNR stored locomotives for a bit in case of requirements. Here's a picture of a CPR locomotive stored:
**LINK**
(courtesy of Ray Kennedy's web pages)
Note the lack of coupling rods, the return crank still there, but the crank rod is not attached. I think, if you look at the front of the cab, the "thickness" of the running boards is due to the connecting rod being placed there.
You don't want the motion work, or the pistons moving about for a number of reasons; pumping of air, lack of lubrication (even if mechanical lubricator, the oil should go in with steam to keep it very liquid, and going to the right places)