Multi voltage power source and negative dc line
If you want to be able to also use battery power in the long-term, you're going to need a solution that accepts only positive high voltage and produces all 3 required rails.

Fortunately, your module accepts up to ±18V rails without running it at absolute maximum ratings, so I would look into a switched capacitor voltage converter that can handle +18V and convert it into -18V.

For the logic rail, you can either look into a buck converter (switching voltage regulator) or a linear 3.3V regulator that accepts up to +18V input.  The downside of a regulator is that to drop 18V to 3.3 is going to make a lot of heat.  The downside of a switching regulator is that the switching can induce some noise in the output lines, and pre-made board units are generally more expensive than regulator ICs.  Both can be overcome.

Why 18V?  Well, you mentioned battery power.  Now, you can generate 15V with 10 AA or AAA batteries, or you can use two 9V batteries in series to get 18V.  The Teensy processor has a max draw of 200mA, and the input module only 8mA, so two 9Vs should give you around 2-3 hours of life (based on 400-600mAh)

You then connect everything in parallel, giving you +18V from the battery/PSU, -18V from the converter, and +3.3V from the regulator (switched or linear).