Kitchen Gas Appliances - Clean BETWEEN inside/outside glass on oven stove door?

As I write this, my TAPPAN free-standing gas stove is in the self-cleaning cycle for the oven. Somehow or another, however, gunk has accumulated BETWEEN the outside glass door and the inside glass window. (Believe it or not, I even see a few spider webs - any spiders are surely zapped by now!). Any suggestions on disassembling the door so I can get at the glasses to clean them (if I should try at all)? Should I try to take the oven door completely off first? Looks like there are screws all around the door that hold the layers together...but is a Do-It-Yourselfer capable of reassembly so that there are no dangerous leaks? Any other potential difficulties/problems I should be aware of? Thanks in advance for any help!

Some of the newer range oven doors slide right off the hinge. If yours does this than you could take it to a workbench and try disassembling the sections. Something , most likely a gasket has failed or it could be just loose screws. A point of caution. reinstalling the door on the hinges can be a bear. When you pull the door off the hinges will spring closed. You have to force them open and put a nail threw the hole in the hinge to keep it open until the door is slipped on. Give it a try. Hope everything I said pertains to your oven.