An interesting question - I have found the answer to be at the ends right after the switch divergence.
An interesting question in return - How do you plan to couple the cars with both ends open?
Your arrangement is more for dropping off and picking up sections of a train (maybe) - rather, than making up sections. You could break up sections, however.
The free version of SCARM would permit enough tracks to create the "yard " with some approach track. It also would permit using the simulator to test if this track arrangement will do what you what it to do.
here's a Ross 3-way yard throat for an elegant way to do it in about 26" on each end.
