Update - my constant calls and emails have been noticed. PEBLO just called and told me he spoke with VA IDES supervisor and to stay next to phone as they are scheduling all of my appointments at the local VA instead of QTC. He said its possible they could be tomorrow (not hopeful) but "very soon". MAY 1 sep/ret is a no go, but he said JUNE or JULY is possible which means I may not have to turn down this amazing job opportunity if I can get the company to work with me! Let's see what happens now...
eodpete, do some research on "DoD Skill bridge." It's a program that allows you to take an extra 120 days of permissive TDY for things like internships and job shadowing. I'm not sure it will work for your specific scenario, but worth looking into.