Ok well obviously a new one is easier, but here's what I came up with. The little tab that prevents the door from locking while open is only a safety feature. I tested this manually, here's the process.

I held the mechanism that prevents it from locking out of the way and locked the latch. I closed the "door" by spinning the latch two clicks. I unlocked it and opened the "door."

https://vimeo.com/112965017

So I'm gonna cut that mechanism out, enabling me to push to lock down from the inside with the door open.

Granted it will be easier to lock my keys in the car, but I'll make sure to put a hind a key on today.

It helps to talk out loud sometimes.