Voters were asked to select a new head of government for north-western Taoyuan county, a heavily industrialized area of 1.2m people that also contains the island's main international airport.
Delegates from many larger states arguing the plan would have given rival Democrats a head start by allowing them to select their nominee well before Republicans.
MPs on the Business, Innovation and Skills select committee voted against accepting the nomination of Prof Ebdon as the new head of Offa - and called for the recruitment process to begin again.
Wales head coach Gareth Jenkins had sympathy for Henson, but said he could not afford to select unfit or out of form players in his final 30-man squad.