You will need to use your MIDI splitter box with BSP#1. The BSP doesn't do "proper" MIDI THRU so you will need to run around your second BSP off to the synths and drummer you want it to sequence, while still shooting off MIDI for clock BSP#2. If any of your synths and drummachines have proper MIDI THRU ports or echo MIDI IN on the MIDI OUT port (soft-thru), run them on a chain from BSP#2.
Another option is, if are planning to sequence the two of BSP's with their own pads, you can just run a cable from the Master to the Slave using Clock sync. If you run in this manner, you will need to remember to manually reset the Slaved BSP when you stop and want to restart from the top of a sequence.
In both situations you will need to have one of the BSP's run a MIDI chain from it. If none of your instruments have MIDI THRU functionality of any description (physical or soft) you will need a second splitter.
Regarding channels and what not, you are correct about the separate channels per instrument. Although running on two separate MIDI busses, it is still good practice to give all your instruments a unique channel (if you have less than sixteen instruments running of course).