On corruptibility, true, it's not been tested so one can't say one way or the other. But at least in principle it rules out many of the common paths to corruption.
Let's take four major forms corruption takes: (1) a big bag of money dropped on your table. (2) I rub your back, you rub mine, reciprocal relationship. (3) Blackmail. (4) Personal: the desire for power.
(1) is of course still possible, but you're gonna need a lot more bags, and you're gonna have to be very careful with how you approach. Usually, the path to bribing someone requires a "romancing" phase; you have to make sure the other side is open to your proposal and, most importantly, won't give you up. This is a lengthy process that is much easier when the pool of candidates is small and doesn't change very often. How valuable is that bag of money when that person won't have any influence in 4 years' time? You're gonna need a lot more bags, and you're gonna have to be a lot more careful about who to approach.
(2) This one is out of the question. These sort of reciprocal relationships take years to cultivate, and we've immediately removed one of the prime motivating factors which is campaign funding.
(3) Blackmail. This one will still work, but again: you're gonna need a lot more detective work to dig up brand new dirt, every 4 years, on every member of a senate. This becomes very impractical. Also I'm gonna go out on a limb and say the sort of secrets an average sample of the population can be blackmailed on is not the same as that of a small group of career politicians.
(4) Again, mostly out of question. There is a much higher incentive to pass laws that benefit people "like you", but not much you can do to benefit yourself directly (excluding the unlikely chance that the person who drew the lottery ticket is, say, CEO of some large corporation), and still, this only works if by some chance a large proportion of other lottery winners are like you. Otherwise, strategically, the only personal benefit you can get out of a position of power is to pass laws that benefit the country as a whole.
On the definition of Democratic. Yes, that's a fair point. Or perhaps sortition lives in a sort of quantum state being both democratic and dictatorial.
I hope someone manages to test this out. To me it seems obvious that the biggest threat to society is not climate change, or antibiotic resistance, or bad economies or poverty: all of these have a single root cause: corruption.
There's no lack of scientific innovation to solve the other problems; it's corrupt institutions that stand in their way.
Our number one focus as a species right now should be to figure out how eliminate corruption from our institutions and lessen the impact of bad actors.