Well....an update: When I called the dealer I leased from this morning (Kia of Puyallup). I got offered a service slot late NEXT week for diagnosis. I told them that was not acceptable as the car was essentially useless to me and I was told a service advisor would call me back. So far (this has been about four hours) none has.
I also took the car down to the nearest Blink Level 3 charger (2.7 miles away per PlugShare) and found, much to my relief, that I CAN charge it on level 3 (to 80%, of course). So at least I have a way to still use it while I wait to get it "diagnosed". Interestingly I am still getting "charger fault" and sometimes "external charger fault" messages upon starting up, even after coming off the Level 3 (which I've used twice so far today).
I further called another dealer which has a good reputation around here (Lee Johnson in Kirkland) - and was offered a service appointment on May 10th!! I don't know what's going on with Kia service in this area, but something certainly is.
Just now I went back on the leasing dealer's online service scheduling tool and found an opening for Thursday afternoon - so three days from now. That's better than next week. We shall see what happens then.
In the meantime, I have 74% charge when I get back up the hill from the Blink charger at Walgreens, so we have effectively a 60-mile range at the moment (and much more expensive electricity than charging level 2 at home).
On a related note, I got a look at the Niro EV at the other dealer yesterday. Interesting....but starting at over $40K for the base trim.