Probably too late to be "fast", but yes, it's possible. If you had a decent size cage, culled off adults to keep their population low, and other steps, you could probably pull off a one cage cricket system, but it'd be a lot of hassle and you'd have pretty low yields. If you have too many adults, cannibalism would be a big concern, both of the young crickets and the eggs.

As for an incubator, as they've said, it's not necessary. They're usually kept at a higher temp, either through an undertank heat, a heat lamp, or simply a high ambient room temperature to speed up development, but not because it's required. An undertank heater will shave weeks off of the time it takes them to mature. Incidentally, this is also true of most of the tropical roaches people breed.

If you really want a one tank system, I'd consider their advice and go with roaches. Crickets aren't that bad, but they'll definitely take a more effort and space than any standard roach. What sort of yield per week are you wanting with the crickets, out of curiosity?