Here are my thought bubbles.
I find it intriguing that you'd expend so much intellectual effort because you
hate politicians!

I for one have no problem with our political system and method of selection - even when my team doesn't win office! On the whole, when the majority of the populace lose confidence in a government or a leader, the leader will be replaced (by their own party), the senate can block supply or you only have three years to wait to vote them out. Kicking out under performers is easy in Australia (as opposed to say the US) and to me this is an overarching consideration, regardless of how the representatives are chosen. Fixed term parliaments would work against such mechanisms.
Your proposal is rife with committees, conventions, elections, discussion and survivor style eliminations, but you expect this to happen politely without lobbying, ideology or politics (= a particular set of political beliefs or principles) and spread over a year or more?

Granted, it would make good reality TV ... who will get eliminated THIS week?? But the thought of having such an extended election cycle makes me want to vomit.

That this would somehow be a cleaner and less corruptable process is fantasy IMO.
You stress the use of a Jury process. However, a jury only works in a court of law because of strictly defined parameters of decision making and interpretation and adjudication of evidence. No such parameters would exist for the 25 or 100 strong juries you propose (one for each electorate!

). It would be a free for all. Cliques would invariably develop based on common interests, agendas, politics (= a particular set of political beliefs or principles), ideology and driven by type A personalities. Sound familiar? This will happen no matter how random your selection of the original jurors. It’s human nature for Pete's sake!
As far as I can tell, your system will have zero impact on the quality of candidates. In fact, I'd actually expect a more amateurish field of candidates who are not bound together by a common / uniting platform (ie views, beliefs, goals, strategies, plans, policies) and with little or no governance experience (since you don't want professional politicians or parties). Consequently, you'll end up with a disparate bunch of people in parliament with little experience, negotiation skills and all with
different fixed, dogmatic and unyielding views - a recipe for complete stalemate and disarray in government!
Finally, I think your glass is half empty. Look where you live! Australia is ranked by the OECD as the No. 1 country in the world to be! Each of the countries in the OECD are ranked according to the ‘better life index’. If a country's well being is high (based on these factors
http://stats.oecd.org/Index.aspx?DataSetCode=BLI#) then it's governance, on the whole, must also be healthy - by definition! Australia is No. 1!!! Why mess with that? Because you hate a single profession?