I suggest using a cyclical random military-style draft of citizen volunteers to fill government offices outside of the presidency.
The draft pool would primarily consist of a pool of adult volunteers in good legal standing and with adequate experience and/or education for a given office. The pool would only use non-volunteers when there was a shortage of volunteers.
The Cycle of service would consist of 4 phases varying in duration depending on the position being served.
1. Apprenticeship - A duration to train for the position
2. Acting - A duration serving in the position
3. Mentor - A duration to train/prepare other apprentices
4. Civilian Transition - A duration to transition back to Civilian life/work.
Short terms reduce bias, vested interest, constant re-election focus