First trip back - they couldn't find the hole so they dismounted the tire, cleaned the rim, and remounted. The tire still leaked.
Second trip back, they found the hole. A nearly new Eagle LS was rolled out and mounted. 24 hours later and it's still holding fine.
I still bought 4 tires with 70% or better tread for about 75% less than new. The added hassle of two trips to the tire store sucked, but I had some free time. If they last 12 months, they'll be worth it.