Ummmm, really not trying to rain on your parade but…. please correct me if I’m wrong in following the chain of events here. Lowfire clay, glazed with cone 6 glazes but only fired to 06 then reglazed with 06 glaze and fired again? Did I get that right?
If the above is what happened I would keep those pieces for posterity sake but not use them as the clay and glaze are both imature. If you want to check my theory take the vase, fill it with water and stand it on a piece of newsprint for a couple days, I have a strong suspicion the paper will be wrinkled from the vase leaking. This isn’t that big a deal, you can always put in on a coaster to save your furniture. But, the green matte glaze on your mugs looks like it isn’t fully melted and therefore more prone to leach. If so you will be ingesting some of the glaze with your bevvy. I would take a slice of lemon or lime, place it cut side down on the mug, put a bit of plastic /saran wrap overtop and leave it sit like that for a day or two. Rinse it off, dry it well and see if you can see an outline of the lemon or any change in colour of the glaze where the lemon was. Also, the mugs, as is the vase, will be porous, overtime they will soak up water from doing the washing up or the dishwasher and the glaze will craze. No biggie for the vase but the mugs will also get very hot in the microwave from the water that has soaked into the clay.
(Sorry to sound like a killjoy, I'll go hide for a while now)