Hi Hatari,
One important point (you may already know) when there is full load Toyota suggests make sure your tyre pressure measured accurately. Front tyres 33psi, rear tyres 34psi, this is measurement when you check cold tyre pressure thats when you have not travelled 10km still, best time is morning. I suggest you can maintain 34psi for all tyres as cold tyre pressure.
I never noticed Innova hitting bumps or any rocks even while travelling very very bad roads. Already I travelled in my Innova very bad mud roads in hilly areas. Swift used to touch ground sometimes but this Innova (although as per tech. spec swift's ground clearence 170mm and Innova's 176mm as I read in mannual..) never touched because of its highly stable suspension make Innova ride solid without hitting any obstacles like road hump, rocks etc..
Since Innova is heavy car I feel it all depends on tyre pressure and since it has 176mm ground clearence one can't drive fast in bad roads because
it will hit rocks in sush cases, IF road is very bad drive slowly things should be alright

Please check for any loose parts under engine or front/rear suspension unit. Toyota can help you thats one best solution. Please get in touch with them, I always reecived good answers from them so far.
Regards,
Ravi.