I have done something similar to power portable speakers....
( same principle, different voltage :-) )
using a buck converter gives much more voltage stability than
what the scopes are designed for....
A "12v" lead acid or SLA battery can vary from 11 volts and close to 14 while still able to pump out lots of current....
So this solution is actually better...since you will be regulating
the output to be a constant voltage
At risk of repeating what others have said....
Steer away from Linear Voltage regulation - its simpler but wasteful of battery power. Any of the ones that Bojan suggested will work - i'd go for something with at least a 3A max output current to maintain voltage stability during slewing. (tracking uses bugger all, so don't worry about that bit) (and the 20 amp job is overkill)
There are 2 things that might fly up the ointment....
1.) the capacity of your drill batteries.
Some are not great for endurance - they are designed to supply
large current for a small time. (think how long you actually power a
drill). I'd suggest you need at least 4AH so that you don't have to swap
batteries halfway through the night.
2.) there will be little to no warning of impending battery flatness. SLA's slowly drop voltage as they fade, so you will start to see things like slewing causing the lights on the controller dimming. Lithium ion and the like, tend to pump out max until they don't. especially if you have good quality drill batteries with built in under voltage protection.
Overall though - it works well with my speakers, and i don't see why it
wouldn't work well with your scope.
P.S.
depending on your battery, you might be able to buy an adaptor to effect the physical connection -
something like this:
https://www.ebay.com.au/itm/40265968...CABEgLnAPD_BwE
I know dewalt and makita sell off the shelf adaptors to fit their batteries - note that these don't change the output voltage - you will still need a buck converter.
(some also have USB power out)