I know the wet season is December-April, and January may be too flooded. So which month will I have the best chance to see the reflection? December is the most convenient for me, but I'd rather feel confident I'll get to see the reflection if the best time is another month.
You are quite correct about the wet season but even during this time you take pot luck. This month (February) has been very wet here in Santa Cruz (Bolivia) but I cannot vouch for Uyuni. I took a three day tour in July last year and, despite there being no standing water, it was still beautiful, particularly when we got up to some of the high altitude lakes and volcanic fields.
March and April are the best times, but wet season can extend to April sometimes. Recommend book tour ahead of time. www.bolivianlife.com/bolivia-salt-flats-tour-with-red-planet-expedition/ is a useful web site giving you lots of good info about what to wear, take, risk of sun burn, the cold, etc.
Really worth the visit-not much to do in Uyuni itself though.