Is there anyone with a DEEP understanding of COBRA?

I will be laid off at the end of July (at least I got some notice) but I can go onto my wife’s medical plan. I have several chronic conditions that require monthly prescriptions and quarterly blood tests. Question is she works for our State and their window ends on June 30th. Can I enroll even though my coverage will stay in place until July 31st and what happens with pre-existing conditions in transferring coverage?: I know double coverage is legal so I don’t have to withdraw on June 30 from our current plan. Question is whether I can join the State plan on August 1 and get around their “window””” due to a qualifyiing event under COBRA. I can call the broker tomorrow but I am very anxious about this this morning