Easy enough hybrid fix; those people that are judged to perform well in direct sortition local area politics who also wish to further that work are in the pool for a combination draw|election for state roles .. and then tier upwards to national.

The general public get to know their national candidates first at the local and then state level, and those candidates are judged as "better than a head of lettuce" by their peers in office.

The political wing of government is essentially (ideally) just about debating policy - it's the civil service, military, and judicial wings that get tasked with making things happen (subject to checks and balances).