I’m worried that sort of thing ends up like Jury Duty where anyone actually qualified to think deeply about the case is doing everything in their power specifically to not be selected and waste their time. The pay is shockingly low and it can be a huge disrupter if you run your own small business.
IMO you'd want this to pay pretty well, like 95th percentile income, to help ensure that most people would actually _want_ to serve.
Just give it the same income as current congress representatives. That's already a 90th percentile income.
95th%ile income, given to people with randomly distributed incomes? first law they pass: "we get to keep this job, we need to get rid of sortition, it'll never work!"
This is a strawman. Since this body would be organized by the constitution, it can trivially eliminate that risk by just setting a duration of their term, which they would not be able to overturn.