Congrats to GlazeyLady for the win! My strategy was very similar.
Sim A money making skills:
Wk 1: singing and piano
Wk 2: fishing and programming
Wk 3: handiness and DJ mixing
Wk 4: gardening and guitar
Sim B money making skills:
Wk 1: writing and violin
Wk 2: mixology and video gaming
Wk 3: charisma and logic
Wk 4: painting and photography
First and foremost, my sims needed to get the lot/inventory value as high as possible to increase the bills. Painting is the best way I've found to add value without a career or retail store. Both my sims painted (sim A never sold any of hers) and to boost the painting values both sims also had the marketable and creative visionary traits. This was the only skill I didn't max in the designated week because it was maxed long before week 4.
I also split the skills that would bring in most of the money between the four weeks with the biggest money makers in the final two to cover the last two bills. In my playthrough, writing carried week 1 for the same reason Glazey mentioned, mixology/residual royalties covered week 2, handiness/charisma/residual royalties carried week 3, and painting covered week 4.
Once my sims had made enough money with their designated skills for the week (and maxed them in the process), they painted (storing finished paintings in their personal inventories) until the bills were delivered.
I used a club to manage needs and provide skill/moodlet boosts. I never moved, and I didn't use the wishing well (I really should play test with it one of these days).
Thanks again to the challenge team