Well, although that was my understanding, the real world experience was different.
Using the CTRL register as defined above and transitioning the CTRL pin low to high only produced a TRI SWEEP response. However, if I pulsed CTRL low-high-low (exceeding the minimum high time spec) WITH NO OTHER CHANGE then I was able to obtain a SAW SWEEP response.
Before I tried the CTRL pin pulse, I tried every combination of 0xE07 to 0xEF7 and nothing produced a SAW SWEEP (I know, some of those combinations don't produce an auto sweep at all). Any sweep I obtained was the TRI SWEEP.
ONLY by pulsing the CTRL pin was I successful at producing a SAW SWEEP.