The linked discussion is right about it being kept unstrung. It will ruin the bow if carried around strung or too long, especially in any kind of heat.
That being said, the longbow was primarily a weapon of war, not for hunting, although it was used. As an archer myself, the unfortunate truth is really the easiest way to carry it is to just rest it on a shoulder. They would usually, for transport, have the wrapped in an oiled wool or linen bag, like a giant sock, to protect the wood from moisture. You could rig up a half length wrap on a baldric or other harness to strap it to you back so it would be visible.
As a participant at local faires I try to carry mine only during parades, gigs, and to the field for shooting. They are long and ackward in a crowd.