Due to the voltage drop from a long cable or a poorly smoothed or regulated supply the operating conditions wont be at all similar to operating your motor controller from batteries, as intended in the final application.
You'd probably do better to source four used 12V Lead Acid car batteries of similar capacity, which could be in relatively poor condition as long as they can still hold a charge and don't have any dead cells so hopefully would be fairly cheap. Batteries with removable caps so you can check the acid level and top up with distilled water are preferable but they are fairly rare nowadays.
Connect them in series to get a ripple free nominal 48V, that closely resembles the output of your proposed LiPO pack. The load circuit should either be fused or have an appropriately DC rated circuit breaker, with the fuse or breaker rated to interrupt a minimum of 60V DC, as such a set of batteries even in poor condition could put a very large current through a short, and there is a risk of explosion if you short a recently charged Lead Acid battery and there is a cracked internal connection that cant carry the full short circuit current, or if the electrolyte boils due to Joule heating.
Then you need to charge them - you could do so one at a time from a CC/CV bench supply with a series Schottky diode to prevent reverse current if input power is lost, or you could build a charger for them - probably the easiest would be 48V RMS from your transformers, a bridge rectifier and a series ballast resistor to limit the maximum charging current + a relay to disconnect its input power when fully charged. Due to the unknown history of the batteries they are likely to have dissimilar actual capacities so will require balancing - for that you can simply add a shunt regulator across each one set to about 14V, that can pass the full charger output current. Detect when all four shunt regulators are passing significant current, and start a timer to terminate the charge using the relay and disconnect the shunt regulators. Charging should ONLY be performed with adequate ventilation. Alternatively if you can obtain four small smart float chargers for Lead Acid batteries, with two wire mains leads (no ground), simply connect one across each 12V battery.