I cleaned the capping station and wiper (Dana's video was very helpful in that regard, thank you). No dice.
I bought Piezo flush and an extra set of cartidges, as well as the adjustment program. I am going to to do an initial fill, disconnect for 48 hours, another initial fill and then give this a last try. If they don't come back after that it's probably hardware related.
When I bought the printer I had the foresight to get an extra 3 year warranty, which expires in September 2017, from the retailer. So I should be covered. I guess with the 3880 now discontinued, they'll refund me the original price paid and I'll have to get a P800?
Is the P800 compatible with the cartridges I have?