So obviously Jess has the "Halting Hex", which halts the game and pretty much skips over an eviction. I believe this would be the absolute BEST move for Jess to make, if someone on the other side of the house (pretty much anyone but Cody, Mark, and Elena) wins HOH, Jess needs to tell the HOH about the Hex.
Step 1: Tell the HOH about the Hex.
Step 2: Claim that the hex is only good for this week and that if them (Jess or Cody) are on the block, or anyone they don't want going home that week, then they will use the hex and skip this week.
Step 3: Give out some options that you would like to see on the block.