Kenny, you are correct in your concern although I have never heard of damage other than minor superficial damage caused by jacking under the crosshead.
Cut a piece of timber and rout a groove in the centre along the length. The groove will prevent the crosshead tube and therefore the car slipping off the wood. Cut the timber to be as wide as possible in order to spread the load.
I use also a piece of plywood to put between the rear crossmember and on the chassis sides. It prevents damage.
