Share a dryer vent with a portable A/C unit

In theory that is a legitimate option. The usual problem though is there is insulation behind the blocking that would obstruct any air flow. Retrofitting the necessary baffles to allow air to get past gets to be a lot of work and makes the cold spots at the eave even colder.

It sounds like you may have adequate ventilation except for the lack of benefit from the stack effect by having high and low vents. This of course is a good thing to strive for, but I'm questioning if it's really worth it if the existing vents are ample. Even if not, adding additional ventilation where it's easier may be a reasonable compromise to the ideal high/low configuration.

You would need to run an inspection camera through it in order to identify exactly where the break or clog is. Though, as the comments suggest, often it's easier and cheaper to just run a cleaning tool through to unclog it versus first running an inspection camera through.

I would probably only resort to an inspection camera if it became a chronic problem, which would suggest an issue in the pipe (sharp bend, collapse, etc.). If it has only clogged once, and you've never cleaned it before, its quite possible it just clogged from normal use over a long time.