You've mis-understood how the PP-DMX20L is set up and operates.
The PP-DMX20L behaves the same way as a DP-DMX20L:
You have a pre-programmed mode, which is not what you want right now.
There are 3 DMX modes:
1 channel, in which all 4 channels behave as one large bank
2 channel. This time channels 1 and 2 behave as a single channel, while 3 and 4 behave as a second channel.
4 channel mode: Where each channel responds on its own.
Based on your description, you need to go to 4-channel mode. It sounds like you send your starting channel right, so you're in good shape for starting out. Go to 4 channel mode and you'll be all taken care of.
So, you CAN do what you want to do. That's the good news, it's easy to do. The other good news is that you just need a minor reconfiguration to the PP-DMX20L. Easy to do, just hit the mode button I think.
Have fun. Let us know how it goes.