That looks awfully like a commercial machine; if batteries worked in that particular role in the commercial world, I’d figure they probably have a fairly long lifespan, or they’d have gone with the AC power supply right from the beginning.
Will you have to rewire parts of it to connect the AC adapter? If not, then there’s usually some symbology right around where the AC adapter plugs in that gives you polarity, voltage, etc…
Now that we know what the load is, I would probably start with a 12 V switcher; they’re cheap, light, and can put out gobs of current. It will probably work fine. But if the circuit boards become unstable due to noise on the DC, then there are a couple solutions: stick an electrolytic cap across the DC at the load (which may or may not work), or use a linear supply (which will definitely work).
Another variable is the (electrical) distance between the output of the power supply and the load. If the power supply is near the wall plug, and thus there’s many feet between the output of the power supply and the load, the current pulses will create voltage fluctuations at the load. Whether or not the magnitude of the fluctuations will cause of problem depends on a number of variables. If this is a problem, the solution is to locate the power supply very close to the load.
Sorry if it looks like I am over-analyzing the situation, but I have been “bitten” by these issues many times in the past. I just wanted to make you aware of them in the off-chance the load acts wonky for some reason when powered from a PS.
I’ve ordered a 12 volt plug. We’ll see how it goes.