FWIW the phrasing I use with clients is "fixed-price for successful completion of the following objectives" so it's a bit of a moot point.
I do think you're overstating the research though. Many studies of unconscious priming haven't been replicated, and psychology as a whole is very subject to publication bias. [1]
Anchoring is a real effect, and I'm a fan of Kahneman (especially prospect theory), but the evidence about "incidental" influences is very weak.
(the research I read about was way stronger than just statistically significant, or something like it. I would be pretty shocked if it failed to be replicated. It's a very strong effect.)
The phrasing you say you actually use isn't an anchor. But you can still try different ways of phrasing it!
Extremely subtle differences in phrasing can have huge effects on people's reactions. If people are not reacting reasonably, try a slightly different phrasing, as well as different offers :)
I do think you're overstating the research though. Many studies of unconscious priming haven't been replicated, and psychology as a whole is very subject to publication bias. [1]
Anchoring is a real effect, and I'm a fan of Kahneman (especially prospect theory), but the evidence about "incidental" influences is very weak.
[1] http://www.nature.com/news/over-half-of-psychology-studies-f...