Thanks for the advice everyone. I'm getting the idea that I just need more practice with the Type 9 I'm flying. I should be able to fight the interdiction (I may have given up on that idea too quickly) and I should be able to run if I lose (It was a deadly NPC anaconda that beat me when I tried that).
Here's the build I was flying yesterday:
https://s.orbis.zone/1d-5
I'm a fairly casual player and get a bit panicked and fumbly with the keyboard when the unexpected happens (yes, KB&M here) and I have to switch to "get serious and focus" mode. So, I get that the best move here is to just avoid the whole "dump cargo" thing. I'll work on my escaping and running skills. I don't really mind dying, I just got annoyed with the seeming inevitability of it based on those 4 experiences. (Also, I'm not sure what I was getting hit with - missiles? - but it wasn't lasers or cannons and the damage was quick, shields down, heat high, module damage. In other ships I sometimes fight back. I wasn't used to the speed things happened yesterday.)
But, I still think the NPCs should be just a touch more patient if they are going to demand cargo at all. The option of a "Yes, yes, I'll dump the cargo please don't shoot!" response would be great.