We have our Mountain bike on the toolbox with a $30 Ebay bikerack holder thats lockable. We actually now have 2 of them on there and Motorbike on the rear.
We have been on the road Since April 2012 and the bike has been on there all the time whilst travelling. We use 2 bungee cords to stop the bikes moving around and we have not had any issues at all.
The only thing is that they do get dusty in the lubricated parts but its not an issue as long as you give them a wash and some WD40 when you can.
Ours are not Braced with wood or anything else other than the brackets that came in the kit.
We have been on some rough roads and never had an issue with them moving or breaking anything on the rack or the toolbox.
No need to overthink and over engineer unless your that way inclined.
Stookie