How to make xvnc not kill the session on exit

Use x11vnc, It will attach to a running session and let you share the desktop. If you run it as root to connect to an xdm session, you will need to do some research into Xauth as it can be a bit fiddly to set up.

Edit to add: Karl Runge no longer appears to be maintaining the original x11vnc however development is continuing on github. Or you could do as suggested below by @ivan-talalaev and use x0vncserver.

Another advantage of this server is that it supports alot of the advanced VNC features used by UltraVNC including large bitmap caching and file-transfer.

Can I change any VNC settings to make it run in another session?

Short answer: no.

Long answer: VNC on Windows typically attaches to the existing console session screen and works its magic by intercepting display changes. The protocol does not have any session tracking capability, it simply provides the crude approximation of a "screen scrape", although it is a very efficient one at that. To do what you want, you would have to get VNC to appear as another viable remote desktop protocol alongside RDP (which is what Citrix ICA apparently does), which implies that Windows would still handle your session; the VNC server would simply provide something to render to.