The fact that you’re considering Ableton Push suggests that a computer is part of your setup, because Push is useless without a computer. So I would suggest a different approach entirely: Add an audio interface to your system with lots of inputs and outputs. I’m partial to the Roland Studio-Capture, which has 16 inputs and 10 outputs (i.e., 8 stereo pairs in, 5 out). If you want something with even more capability, I have heard good things about RME, thought I haven’t used their stuff personally.
Then you can connect your various hardware devices to the audio interface. That lets you record each device on a different track at the same time, use them as if they were send/return effects, route audio between them, and so on.
The Octatrack is a fine sampler, but one thing it does not do is allow you to control a large number of inputs.