You did a great job Sober IMO. Way to adjust to changing conditions and get it done. If you would have had a supervisor with you, Im sure they would have told you to do the same thing.
We don't have the hand cart straps either. I just bungee mine to the little wire storage cages in the back behind the drivers seat. No need to buy a bungee, I see them all the time lying on the street. Just pick one up when I can.
It makes sense to have straps for the carts, those things roll all over the place, even when you lay them upside down over a wheel well. I hate that scraping noise they make. They are a saftey hazard for both packages and drivers alike when loose.
Steve, you might ask your mechanics about ordering you a strap or the eye bolts like Scratch mentioned.