On a log truck, the logs are chained around each other, and then sit on the trailer with weight, no chains to the trailer. But, when hauling on a flatbed, chaining to the trailer is a good idea.
How many logs are you transporting at a time? One? Several?
I would probably make some wedges (fixed to the trailer bed somehow) to keep stuff from rolling around, then chain it all down.
A standard binder only has a few inches of pull. A ratchet binder a little more. On occasion I've tightened a load first with a come-a-long, then put the binder on. You can put a cheater on a good binder to make it quite tight.
Another thing. Sometimes it doesn't hurt to start with a chain under your load, so you can wrap it around your load to get a nice tight bundle. It never hurts to plan ahead and put your chain down FIRST.