The cost to redevelop has been estimated at roughly $20.4m, with work to be phased over three years.
The option to demolish and rebuild comes with an estimated price tag of $48m-$52m, meanwhile the permanent closure would cost somewhere in the vicinity of $300,000.
Staff were also instructed to return a report to council no later than June 2016 with the detailed seismic assessment and a recommendation to address the Founders Theatre issues.
Executive director H3 Sean Murray said during question time that although seismic assessment would begin in the next couple of weeks, results were not expected back until the end of June.
"We're not entirely happy with that, however it is difficult to get availability of the specialist engineers for this type of building," he said.
A number of councillors questioned why public consultation would begin before the assessment was completed, but Mr Murray said the $20.4m estimated for a redevelopment was a "worst case scenario" and regardless of the seismic strength of the stage house and auditorium he did not expect the bill to increase.
The fall in patronage from a high in 2008/09 of over 100,000 to last year when patronage was a little over 60,000 was also picked up on, with councillor Garry Mallett pointing out the same period had seen the population of Hamilton increase dramatically.
Mr Murray said the global financial crisis had effected patronage to theatres across the country and increased competition had also played a part, with a number of events like university graduations going to Claudelands.
"We've also had a fairly dramatic increase in the dissatisfaction of theatre goers with the facility, the service, the general comfort and so forth," he said.
The designation of Founders as a regional facility also raised the prospect of ratepayers outside the city contributing, and council chief executive Richard Briggs said it was not unheard of for a facility to be funded not only by the territorial authority where it was located but also by neighbouring authorities.
"I think the Westpac Stadium in Wellington is funded based on distance from the stadium to the next local authority, who pay a proportion of the cost ... It comes down to your relationships and your discussions and so forth with the region of what is appropriate," he said.
The public gallery was packed with those eager to discover the future of Founders, with a number of concerned parties making presentations.
Creative Waikato chairperson Sarah Nathan said the closure had sent shockwaves through the arts community.
"What I would like to speak about today is the flip side of this regrettable situation, and that is a phenomenally exciting and rare opportunity for Hamilton."
She said initial feedback favoured a rebuild.
"We all know there is rarely external money available for old and broken, but there is a strong case for attracting new external money for new and visionary."
She cautioned against "paralysis in election year" and warned of a "slow cultural death" without Founders.
Clarence Street Theatre general manager Jason Wade suggested a theatre on the river bank would fit well with the River Plan.
Hamilton Operatic Society chairperson Fiona Bradley said Claudelands Events Centre would serve as an interim measure, but was not a permanent solution.
"Please make your decisions wisely but make them fast," she said.