Another reason for this sudden use of oil is possibly the quality of oil added at the last oil change.
I have an Avalanche with 205,000 miles and has never used a drop of oil....until my oil change guy forgot and added their "house blend". I noticed that after 1000 miles it used a full quart and I was sad. All those years and never used a drop and now I was a user!
Later I noticed on my receipt he noted that the house blend had been used instead of the Castrol 10/30 that has been in the truck since new.
Anyway, I went back and he changed to my Castrol, and the truck hasn't used a drop since.
Just a thought.