I'm with the others. You can plant trees from a root pruning container system when they are fully leafed out any time of the year as long as supplemental water is supplied. This is because the root system is largely undisturbed. They begin growing immediately because the transplant stress is minimal compared to bare root trees. The saying with bare root trees is "year 1 sleep, year 2 creep, and year 3 leap". They are recovering from the significant transplant shock that first year. When you plant a bare root tree after it is dormant, it has a period for the root system to settle in and begin to recover. It then has a period to adapt to sense and adapt to the new environment slowly when it is not trying to grow. It has an opportunity to redirect energy to where it needs it most for recovery. Even with this, we still have the first year of sleep.
If you plant a bare root tree after it breaks dormancy, you are adding one more significant stress to the tree. That does not mean that some trees won't recover, but it does mean you will have a higher failure rate. Other stresses like insects, disease, or drought will have a bigger impact.
I would wait until next fall after they go dormant. As Native Hunter says, if you have the ability to do so, take as large an area as possible around the roots cutting as few as possible and burlap it for transport. The less roots are disturbed the better and faster your tree will recover and grow. Burlap ball trees do better than bare root trees, but because of the cost of transporting the dirt, most sellers sell bare root unless you are buying from a local orchard. In your case, where they are in your raised bed, try your best to make them as much like Burlap ball trees as possible.
Thanks,
Jack