I split this off because I think it's a worthy topic that isn't specific to the White Sox sell off. My quick .02:
I agree that you probably need to make a more decisive move than they have fairly soon, both because of what Bertz mentions about the diminishing returns of hoarding upper level prospects, and because their point in the competitive cycle it will make sense to be a bit more bold.
The deadline and this deadline in particular is going to be a suboptimal time to make such a move. There's already news stories about how few sellers there might be, and in general the deadline has trended away from splashier moves
In particular, the sellers this year don't have a particularly good match for what the Cubs might want to add. This is not to say there's no one worth trading for, but if you made a list of the profiles the Cubs would be most interested in trading for, the top couple on the list probably don't have a good match to players likely to be traded in July.
Having said that, there are a few interesting names if you start dangling multiple Top 100 names that most orgs will hesitate to give up or even have. For SP, Crochet and Luzardo probably highlight the list. At 3B, if the Rays are open to it and a playoff longshot you could maybe tempt them out of Paredes(especially with their 2 best prospects being 3B at AAA). Robert was mentioned in the other thread and could be worth it even if the fit is suboptimal.