What is the best way to secure my 1969 Coupe to a car hauler trailer? I have heard that there are some sort of slots in the frame into which hooks (hammerhead?) or something can be inserted and then ratcheting tie-downs used perhaps crossed at front and back?

I am heading West first week of May to retrieve my new project from Calgary. It is about 2100 miles from here to Calgary.

I rented a u-haul trailer - front was secured with the wheel tie downs. In the back, I tied down to the half shafts.

Here's a pretty good selection of tie down products.

I cross the front straped through the lower control arms. I have 2 heavy 2 ft long straps with "D" hook ends that I hook the ratchet straps to.
The back I go through the wheel slots with them soft strap sleeves with about a 4 ft strap with "D" hook ends. Or around the 1/2 shafts (A PITA, more possibility of strap wear and some people don't like tieing down from the 1/2 shafts) Also, because the back takes the most force from stopping I put a third strap with a hook end from the back of the trailer to one of the holes in the frame under either door.
I prefer to tie down below the car suspension to absorb bumps. Many miles and no problems.

Just have to agree with Paul.  I just trailered a 74 from Portland to Spokane,not as long a trip as yours, but a good test.  I used a U Haul car hauler  with the straps ratcheted over the front tires and the furnished down chains.  The car didn't budge.

Ray