Any real property owner claiming to be aggrieved by the assessment of such damages or such benefits by the secretary may, not later than six months after the same has been filed, apply to the superior court for the judicial district in which such real property is located for a reassessment of such damages or such benefits so far as the same affect such applicant, and said court, after causing notice of the pendency of such application to be given to said secretary, shall appoint a trial referee to make such reassessment of such damages or such benefits. Such trial referee, having given at least ten days’ notice to the parties interested of the time and place of hearing, shall hear the applicant and said secretary, shall view the real property and take such testimony as the trial referee deems material and shall thereupon reassess such damages and benefits so far as they affect the applicant. If the amount of the reassessment of such damages awarded to any such property owner exceeds the amount of the assessment of such damages by the secretary for the real property, the trial referee shall award to the property owner such appraisal fees as the trial referee determines to be reasonable. If no appeal to the Appellate Court is filed within the time allowed by law, or if one is filed and the proceedings have terminated in a final judgment finding the amount due the real property owner, the clerk shall send a certified copy of the assessment of the secretary and of the judgment to the Comptroller, who shall, upon receipt thereof, draw an order on the Treasurer in favor of the real property owner for the amount due such owner as damages. The pendency of any such application for reassessment shall not prevent or delay the construction of the convention center, the related parking facilities, the on-site related private development or related site preparation or infrastructure improvements. As used in this section and sections 32-658 and 32-659, “trial referee” means a referee appointed pursuant to subdivision (1) or (2) of subsection (a) of section 52-434 and designated a trial referee pursuant to subsection (b) of said section 52-434.