Figured it out myself. There are holes in each hinge for removal pins. I substituted large nails for the pins. Insert a nail in each hinge when the door is open and the door will easily come out when it is almost closed.

I used framing nails that are a little larger than 1/8" in diameter and taped them in place with masking tape. I ground the points off the nails to provide extra margin on both sides of the hinge.

The price of new hinges was about 35% of having the appliance store replace the hinges. We have two "wall ovens" - one a Whirlpool and the other a Kitchen-Aid - and strangely enough both use the same hinges. The oven door hinges are the weakest part of the ovens and we have had to have them replaced before. After paying over a $175 each for the repairs I was shocked to see how quickly they failed. Within 8 months one had to be propped closed with a broom handle and the other with a stool just to keep the doors closed so my wife could use the ovens .. and keep the oven light from staying on all the time.
My wife was ready to call the service people again when I said let me see if I can replace the hinges. I looked at the YouTube videos on oven door hinge replacement and it looked easy enough. I found the replacement hinges so I decided to start with one oven to see if I could do the replacement. It took almost three hours to get the oven door off and the hinges changed. Why? Every demo video on YouTube showed opening the door all the way and flipping over a lock that stopped the door closing at that almost closed point. This allows you lift up on the oven door releasing the hinge arm from the catch so you could slide the oven door away from the body of the oven. Guess what! "These hinges didn’t have that little flip over lock!"
I finally managed to get the door off using a screw driver to help me disengage one of the hinges from the oven itself. The rest of the hinge replacement went exactly like the demo videos described. Now I had to get the door back on the oven.
I held the door as shown on the videos and it slipped right in, but when I tried to close the door the whole thing was too high and bound. Messing with it I finally heard something drop out and onto the floor. I picked up this little apx. 1/8th inch diameters by ¼ inch long pin with a flared crimp on one end. I looked carefully at both hinges with a flashlight and saw that there was a pin like that on one side and not on the other. I slipped the second pin out of the remaining side and suddenly the door closed perfectly. It was then that I realized that the pins acted like the flip over lock! The problem was the new hinges had the pin and the old one did not, and you should not remove the pin from the new ones before you put the door back as it holds the hinge in a tension needed need to fit the door back on (and that tension is strong).
So there is a trick. You will need something to function as those pins, like a 16p finish nail, when you remove the oven door.
I immediately ordered hinges for the second oven .. saving the pins from the first hinge replacement. The second set of hinges arrived two days later and I opened the second oven door and put in the two saved pins – the door lifted off perfectly and 15 minutes later it was back on with new hinges. By the way, I saved the now four little pins in a zip-lock bag and put them with our file of appliance manuals. If I have to replace the hinges again I will have the pins I will need for removing the door.
One other thing I learned was why I believe the original hinges worked for several years while the ones installed by the service guy failed in months! On each of the ovens the service guy had replaced only one of the hinges. You could see the grime on the 4 or 5 year old ones that wasn’t there on the months old ones. I wish I could show you the pictures I took of both hinges (which this site won’t let me add), but the two hinges placed side by side had slightly different length and shaped locking arms (that part that slides into the body of the oven). On that first door I struggled with I couldn’t understand why one side just slid out while the other I had to force out. Looking back it was the old hinge that slid out and I don’t believe it was ever engaged as the locking arm was slightly shorter and a different shape. That would mean one hinge was trying to do the work of two. I replaced both on the two ovens, and I’ll bet my fix will serve for years and not months.
Heck, the hinges are only about $35, so why not do both sides and make the new ones match and work together as a set?

Forgot to include model number.
Kitchenaid KEBS207D. The previously listed WP item was for inner glass part.