While White Giant has the most players, you can usually get trades to go through instantly upon demand, but for a price.
The automated purchasing will likely require you to set a max starting buy price, along with a hefty increase when not filled on the previous attempt.
Likewise, to sell, you will be able to charge more if there is a shortage, so there is also an up side to it, which should largely balance out the issue.
In theory: a shortage of players shouldn't significantly impact the world markets, because the number of countries is constant. The problem seems to stem from automated functions, which may be more out of control for AI countries vs player countries. I have noticed that many prices are pinned at the end of their range from shortages lasting a long time.