When I've been using my Logic8 I generally capture at 4 or 10 MHz and capture 50 or 100 million samples (old version) or 10 seconds duration (later version). The sample rate only changes the resolution of the data so that at 10MHz I can see to within 0.1uS - certainly the s/w I've used doesn't have any automatic baud rate detection.
I'd recommend a 10-20 second capture time and most modern computers are quite happy to handle several million samples at a time to set the capture speed well into the megabit region.
10-20 seconds is way more than the Arduino I'm using as a logic analyser can handle. I'm limited to 1kb of data at a time. But for an arduino, as you can see, it does the job quite well.
I've pretty much abandoned this now and gone the route of using the arduino to measure the voltage and current instead. However one day someone might solve it and post how interface with the ming he units.
I'm suspecting there is call and response going on and I'm looking at data from both parts of the device at the same time.
I even went the route of using the nrf24 wireless chip it also uses, but similar situation, just don't understand the format of the data I'm seeing.