Make the saltwater the night before; one heater and pump in each can. I have a Fluval FX6 canister filter on the tank. I use that and flexible vinyl hose to pump water out of the tank and down the commode. Then I use a pump to pump water in from the trash cans (using different flexible vinyl hose). I use unions to separate the hose for easy storage. It's a fairly quick process.
I'm always trying to improve my routines, so hope you might use this 2¢ worth of ideas in that spirit.
Heating saltwater for any extended time tends to have a bad effect on it. Pumping for circulation also has this effect. Basically you want to be able to mix it up and use it right there on the spot. (And you can.)
I can imagine some reasons it might not work out, but have you considered dragging the empty Brutes in the house and then pumping RODI into them?
Heating the water to an acceptable temperature (around 65ºF+) while vigorously circulating the water shouldn't take all that long if you have good sized heaters. Just like on the stove, I'd keep a lid on the containers during heating to male it go as quickly as possible. Then take the heaters offline and continue...
For example...
When I do a water change, I mix like this – same for 5 gallons as for 55 – and use the water immediately (as shown):
You can see in my thread how many times I did this:
A Water Change A Day... (Link)
And BTW, I just got my 55 gallon olive barrels "recently" and haven't actually timed mixing with a paddle in them yet (I've only done a full 55 gallons once)....but it's actually not too much longer than five gallons.
Unless you take some effort to mount them for maximum effect in your mixing barrels, pumps are actually very mediocre mixers. I tested lots of pumps in lots of configurations, and here's the 1000gph propeller pump that worked best out of that field of tests:
No better than the mixing paddle in the first video and 100% more bother to use. The paddle is very simple and quick to use and put away. No unwinding or hooking up or mounting....pure simple.
Another option is to insulate your container with some construction foam and heat the RODI water to a decent minimum like 60ºF continuously. That way it's always ready for use with minimal-to-no heating required.