This sounds exactly like what happened to my 3800 recently. There is a thread on this forum somewhere that discusses this. The best suggestion I heard was that there is a problem with the mechanism that switches between MK and PK inks, which lets it leak all over. I went through two PK cartridges that each in just a few days dumped all their ink out, with some going onto prints (mostly margins). Both cartridges still read as "full" on the Epson Print Monitor, but they were obviously completely empty.
The suggestion was to take it to an Epson repair center where the offending device can be easily replaced and isn't fearsomely expensive.
My 3800 (NOT the 3880) was old enough that I decided to upgrade to a new SureColor P800 while there was a $300 rebate available.
If you are not too far from an Epson repair facility, I would call them and make inquiries.
As I was writing this, Schertz responded with exactly what I was talking about. I think he may have been the one who commented in that other thread.
I did try switching between PK and MK a couple of times, and that worked for about a week in my case, but then the problem got much worse, and finally spilled ink all over a 13x19" print that a client had ordered. That's when I put the P800 into service.