Put the off-putting section towards the end, if not at the very end. The IKEA effect, Loss aversion and Cognitive dissonance are all cognitive biases that provide the backing for this.
The IKEA effect
To quote Wikipedia:
The IKEA effect is a cognitive bias that occurs when consumers place a disproportionately high value on products they partially created.
In your case, users will attribute more value to the work they have already done, and the more work the more value.
Kahneman popular definition is focused on gains and losses that are similar. Although you can interpret it that way in your case, it is safer to define loss aversion simply as:
People's tendency to avert loss
This in itself can be explained by either pain aversion or cognitive dissonance.
Similar to the IKEA effect, after doing work filling many details, abandoning the process would be considered loss, which users are likely to avert.
An excellent example for this is given in Universal Principle of Design1:
Perhaps the most successful use of cognitive dissonance in the history
of advertising is the AOL free-hours campaign delivered on CD-ROM. The incentive to try AOL is provided in the form of a free trial period. People who try the service go through a set-up process, where they define unique e-mail addresses, screen names, and passwords, investing time and energy to get it all to work. The greater the time and energy invested during this trial period, the greater the cognitive dissonance at the time of expiration. Since the compensation to engage
in this activity was minimal, the way most people alleviate the dissonance is to have positive feelings about the service—which leads to paid subscriptions.
I'm a bit worried you suspect rather than know that the section in question is off-putting. In my view, something like this should go through evaluation using analytics.
1William Lidwell, Kritina Holden, Jill Butler (2003) Universal Principles of Design: 100 Ways to Enhance Usability, Influence Perception, Increase Appeal, Make Better Design Decisions, and Teach Through Design, : Rockport Publishers.