That puts my mind at ease a lil bit. Tell me what you think of this. This is the pic I received about an hour ago. It just made me cringe to see it Doesn't look safe or stable. Just don't want my bike to get damaged in the process.
I have done it a million times as well with no problem. Usually I like to have the bike as strait up and down as possible, but if your are tied to the handlebar on each side (like it appears yours is) tight you should be good to go.
I'd be more worried about that big box falling over onto the bike... things that can fall over in a trailer, regardless of how steady they appear to be at rest, will fall, shift, or move exactly the way you don't want them to...
I'd find some way to keep the front wheel from shifting around. I always use a chock when I have to trailer a bike. If you don't have a chock some 2x4 cribbing will do. Leave some spring in the forks also, don't crank the tiedowns all the way down. Good luck