Start a course form a different location is it possible?

You mean it's a circle, that you'll completely finish, just start at a different point of it? I also wonder how can this be done.

Yes a 13 mile circle, start depends where I park, one spot is free but might be full other is paid.

Maybe it's worth to post a feature-request about this to Garmin. It should be easy relatively IMHO, 'cause I think this detection of courses is done in the Connect IQ backend, so once they improve it it'll just work for all devices, all sports...
www.garmin.com/.../

I've had this situation multiple times

Yes, you can start form a different location, no problem. It will automatically pick up where you start, however at the end of course, it will report completed. You then need to start the course again, so that it will bring you back to you real starting point.