Greenman,
I have thought about this more than you can ever imagine.
No matter what you do, it is time consuming. Even a spreader with a shield, only holds so much, and you have to refill it. The shield doesn't do the best job on narrow (36" wide) walks. I've tried a hand truck with (2) 80# bags on it, and a coffee can. That sucked. With 2 men, it would be much easier. Then one could follow the other with a truck, or a hand truck to keep filling the spreader.
Rock salt, is too large to work in a drop spreader. Pellets may work, but they hold even less than a broadcast spreader.
I am assuming the Lesco is a commercial spreader. I know Lesco is "commercial" in name, never saw one of their spreaders. When I worked at a local school, they bought less than commercial grade spreaders for salt, and they twisted the "agitator" pin around the shaft after going 5 feet with rock salt in them. It was a cotter pin they used. I drilled out the hole in the shafts larger, and put in finishing nails instead. They held up better. In fact, they never bent or twisted. I also cut the bottom out of plastic milk crates to make a screen for each spreader, to stop large clumps from getting in them. That too helped a lot.
Just be careful, because many spreaders are designed for seed and fertilizer, and can't handle hard salt.
My problem may have been worse than yours, since we had walks to salt on a 12 acre site. Just the long walks around the edge of the property was a task in itself to salt.
I think the best would have been a drop spreader for that site, towed behind a small John Deere tractor they had. I just never got time to make it. Drew up a bunch of blueprints and sketches for it, but never made it.
I kept the sketches, cause who knows, maybe some day.....
~Chuck