This an interesting situation. You can partly solve Copper Pour issue by changing Flood Over parameter to Thermal Connections, however doing this will not solve the problem of the trace coming to the center of Via or a Pad.
I suggest to change the pad stack to be Annual ring style and print just the Pad/Vias on a clear film and tape it to board prior to drilling and use it as your guide.
You can try importing the gerbers and the drill files in a gerber viewer and print from there. You would print the layers overlapped with the drill. GC Prevue is free and can do the job.
This has been a request for a very long time. OrCad have been able to do this for many years.
See mentor Idea D12012. There used to be a nother idea D7947, but this is removed from the list for some reason.