My strategy was also similar to Minnie. Both my sims started with the soulmate aspiration. My doctor got the connections reward so she could start diagnosing patients on her first day of work. My detective went with the entrepreneurial and observant rewards because the career rewards that come with the second promotion are worth over 4000 simoleons (I didn't want to skip it).
I focused on the doctor career as well because you can diagnose/treat far more patients in a workday that you can jail perpetrators (plus I'm familiar with the symptoms so I knew what to look for and could diagnose them myself in the waiting room sometimes). To treat as many as possible, my doctor always stayed late, ignored patients that weren't exhibiting any symptoms, focused on children first (they won't need surgeries so treatment is faster), and ignored house calls.
The biggest time saver I discovered in testing was to always cancel the admit to exam bed interaction once it had been started. Before I started doing that, my doctor would often go stand beside a bed that already had a patient in it and waste time until finally finding an empty bed. If you cancel the interaction to go run a test on someone else or admit the next person in line, the canceled patient will autonomously go find an empty bed. She managed to diagnose/treat 81 patients by the time elder stage hit even with getting stuck on level 8 (no sim in labor ever showed up).
My detective was far less successful. He never made it beyond level 3. Every time I issued an APB, the perpetrator was nowhere to be found. He added nothing to the multiplier, but he always stayed late to make those extra simoleons.
Thanks again to the challenge team for putting this together. I had a lot of fun.
