Visiting the page, I'm seeing fewer anchor issues than I'd seen previously, but still seeing some like the following:
'Students Keep "No Platforming" Contentious Speakers. Should They Stop?'
'Should Businesses Deny Service to Trump Administration Officials?'
'Is Science Political?'
Some of these can't be phrased any other way, but a little tuning might help: the latter, for example, has a subtle bias towards science being apolitical, and introduces a new claim: that science may be political. Rephrasing the question 'Is science political or apolitical?' would leave you with only an ordering anchor bias - a slight weighting towards the first item in the list.
This also seems to be a factor in the foundational claim made in each question: it usually picks one side or the other, and all arguments and counterarguments are then firmly grounded in that claim. Perhaps expressing each claim as both a positive and negative claim would make a difference.
For example, in the 'no-platforming' question, the foundational claim is 'Social justice movements should abandon the use of no-platforming at universities'. If there were a way to present both claims as foundational - 'should abandon' vs. 'should embrace', e.g. - you would get a more fleshed-out debate, as the arguments for and against the one are not necessarily arguments against and for the other, respectively.
EDIT: I do see you've added what you call 'multi-thesis debates', this seems to tackle the latter half of this post fairly directly.