Those fork mounts work fine mounted on a 2x6 or even a square of plywood. It just needs to be large enough to provide side to side stability.

Make sure your bike fits lengthwise and vertically in the space. Also that one is made for a typical quick release fork with 100mm spacing. You'd need a different kind for thru axle fork.

Ive carried bikes that way for many years in the back of our suburban and pickup. If the bike is too long, you can angle it but that does add instability,. The straighter it is the better.

I also recommend putting the fork mounts at the rear of the vehicle instead of forward. It's easier to roll they bike in on the rear wheel then attach the fork.