Hi, 

You are doing the right steps by trying to prune out what you can. Just trim down to the next-lowest junction, not necessarily any further and dispose of the trimmings (don't compost).

Is it an edible plum or ornamental? If it is ornamental variety, try to just remove all you can, it shouldn't kill the tree by removing it all. If it is an edible plum then you can try to follow a schedule for spraying but will need to be vigilant with it. You can find details for spraying in the Virginia Tech publication (page 16).

While use of a fungicide might be reasonably successful, they can be preventative only (not curative) and may still fail to work some years when infection pressure is high due to weather conditions or a nearby alternate host laden with spores. Multiple treatments would need to be applied each year, starting around early spring. Fungicides might risk harm to other organisms, so we tend to discourage their use; plus, they must be applied vigilantly (according to label directions) since a missed re-application can give spores an opportunity to infect.

If you find that management is too cumbersome for an ornamental variety, you may want to consider a different type of flowering tree that isn't susceptible to many diseases.  

Let us know if you have more questions with this. 

Emily