I finally figured out how to manually route a trace from a reuse block.

Set the Routing Mode to Ignore

I'd created a reuse block and added five instances to my project and it all worked great except EasyEDA Pro refused to let me route a trace across the board boundary containing each reuse block. If routing starting from a pad within the reuse block the trace would bend and twist at the board outine and refuse to cross it. Similarly if starting the trace outside the reuse block and attempting to enter it the trace would effectively bounce off the board outline and go anywhere but the intended pad on the reuse block.

I tried AutoRoute to see if it could do any better and after a very long over night run I found that AutoRoute could route traces to/from the reuse block so I knew it must be possible, even with the reuse blocks I'd created.

I finally tried setting the routing mode to ignore and my traces immediately achieved a super power of being able to cross the reuse block board outline!!! Hope this helps others give their reuse blocks similar superpowers.

It's worth noting that a DRC error is introduced everytime you use this technique to cross the reuse board outline with a trace. But at least there a way to get the reuse block routed.