Personally i'd make a bracket to bolt the top of the HS to the crossbar on the case.
Not a string or some such, but an actual chunk of steel that won't flex or anything, cut slots for the bolt/screw holes so that tightening it down doesn't put a load on the HS.
Once you'd got that bolted on (with the mobo sitting flat, not upright like it is in use) the mobo won't have to support much at all and shouldn't have a problem traveling.