I had the same problem for years, and then my most recent purchase gave me a trailer that was properly sized so that I could use standard transom tie-downs. Love them.
a long shanked eye hook on each end of the bunks
While the eye hooks would allow you to use standard transom tie-downs...I don't see where the eye hook would give you ANY real strength. A big bump; God forbid a front-end crash; all sorts of places where we count on the tie-downs to do their job, would be compromised with a simple eye hook turned into a wooden bunk. I wouldn't do it.
At one time, I did own a boat that had 2 large metal plates that were screwed into the bunks to act as tie-down points. The screws that held them in place were falling out when I bought the boat. Small screws; wet bunks; no wonder they were falling out.
As far as making a more efficient use of an "over-the-boat" strap...I wonder if a standard transom tie-down could be bolted on one side of the trailer side channel. Then, the matching transom tiedown could be affixed to the opposite trailer channel.
A properly sized long strap could have big hooks on both ends. Each hook would connect to the two "transom/now side-channel/ tiedowns". If everything was properly sized, only one auto-tiedown would have to be tightened.
The transom tie-downs that I use are spring loaded so they would slide up into their own "pocket" when not in use. You'd have to stow the longer hook-equipped strap but that is all.
I have never done what I described above, but I do think it would work. I am not sure if buying two transom tie-downs and rigging up a double-hooked middle strap is worth it, but each boater is different.
I know I love the quick on and off of my transom tie-downs. I LINKed my transom tie-downs below, just for reference.
https://smile.amazon.com/gp/product/B00P3IAYSC/ref=oh_aui_search_detailpage?ie=UTF8&psc=1