I am highly qualified but unemployed for a job that may asks for my most recent construction salary which I am afraid may scare hiring construction managers away. What do I do?

If you want to be considered for the job, I think you have to include the accurate construction salary information that's been requested.   Under "current construction salary history, I think you have to list $70K as your most recent construction salary.  But based on the way you wrote your message, it doesn't sound like you're working now.  If that's the case, under the heading of "desired construction salary" I think you should write that your construction salary is negotiable within the $X to $Y range.  "construction salary" and "total compensation" are two distinctly different amounts