Hey CJ, 1 qt/thousand miles could be worn out engine leaking, or rings not sealing. Not Valdeze, not no compression at all, but somewhere in between. Do you have puddles were you park? If not, then what's your compression? Between those two, plus a plug reading, it should give a quick and easy indication of where the oil's going, well short of a, pardon the pun, short block.
I'm thinking puddles base on the lack of blue smoke I saw last Sunday. I worked on my daughter's car this morning, and talk about Valdeze!