You can set on what line on the screen less (the pager program man uses by default) puts search results with the -jn/–jump-target=n option. For example, using .5 as a value for n makes less focus the line with the search result on the center of the screen. This should help with your overshoot issue.
Either set the option within less with the - command followed by j.5↵ for the current running instance of less, or set and export the LESS environment variable inside your ~/.bashrc to have less always behave that way.