These are both exactly what I had in mind. DITF was specifically something I'd definitely read about but couldn't remember the name for. Also think this reply correctly identifies that anchoring bias is the underlying more generic version of this effect / tactic.

Thanks!

Edit: Specifically, reading through https://en.wikipedia.org/wiki/Negotiation#Tactics, I believe both the "Highball/Low-ball or Ambit claim" and "Anchoring" sections describe the phenomena I was thinking of.