Hmmmmm....
Well, OK, so hauling a Speedster on a flatbed like that would not be my first choice but I'm sure there are other factors involved so here's my take:
Buy a flatbed utility trailer with "D" ring strap or chain anchors already welded on. You will need four really strong anchor points at the four corners. The anchor points on my car hauler trailer were "D" rings welded to the deck structure itself and they roughly lined up with the center of the car's wheel track. They could be spaced wider or narrower than that on the trailer with no problem, so it depends on what area you have to work with. They have to be strong enough to take a 3+ inch tie-down strap or chain binder cinched really tight and positioned such that the strap is not otherwise touching a trailer part, like stretched over a floor lip (that could chafe the strap and cut into it - Not good).
If you really want to run wheel basket straps you will need four additional anchors on the opposite sides of the wheels to firmly hold the baskets in place. I would definitely NOT screw the anchors just through the wood floor unless it also goes through the metal sub-frame - You need all the strength you can get on those anchors.
Personally, I wouldn't use wheel baskets on a trailer like that. I would use 3+ inch wide tie-down straps. At the front, I would run a strap up over the lower torsion bar just inside of the shock absorber tower. Do that on both sides and crank them down until the car lowers an inch or so on the shocks.
At the rear, run the straps up over the frame horns that support the engine, pull them back against the engine mount and the ends back to the deck anchors.
DO NOT RUN THE REAR STRAPS OVER THE WHEEL AXLES!!!
There are straps available that have "D" rings already sewn in and I recommend using those at both ends of the car. At the rear, you have the option of criss-crossing the straps to the opposing side for more stability IF the straps don't rub on the engine sump. If they do rub, then don't cross them.
If you've read this far, then let me say this: Buying proper straps that won't fall apart causing your car to careen off of the trailer with questionable anchors could certainly begin to get close to the $400 rental of a U-Haul trailer which has all of that stuff included. U-Haul has thought of everything to make your trailering experience, especially for a first-time car hauler person, an easy and safe experience. I highly recommend using that U-Haul trailer to move your car.