Demon: the Descent

This is a long introduction to a short Demon: the Descent question. I think I know the answer, but I want to be sure.

Here's the scenario: Mr. Glass is investigating a location of Infrastructure under the Cover of Zeke. He gets found out and pursued to the roof of the building. He gets shot by the guards and ends up jumping off the roof to escape. Altogether, Zeke ends up with a bullet in his shoulder, several boxes of Lethal Damage, and the Condition Broken Leg. Mr. Glass switches Cover to Jillian to get away and manages to make his escape.

Now here's my question. The rules state that foreign bodies stay inside a demon when they switch Cover, and Damage carries over. Therefore it seems by the rules that Jillian has a bullet in her shoulder but no entry wound, and several boxes of Lethal Damage. It seems that Jillian would need someone to cut her shoulder open to get the bullet out; would that cause more Damage? What about Zeke's Broken Leg and his bullet wound, would Mr. Glass need to spend a couple weeks as Zeke in a cast to heal the Cover's leg?