Wider tires will have a greater load handling capability - i.e max load rating. But the extra 1" width may cause other issues 1.) it may cause an interference with the steer wheels are turned in fully to the right or left. 2.) if the tires are pressed on existing wheels and you will have at lest 1" of the tire steel band extending beyond the wheels, This can cause an issue should the steer tire make contact with a hard object, dock plate curb, metal column, etc. That is the tire band can be bent. 3.) Also, the steering tread width (center of left tire tread width to center of right tire tread dimension) of must be maintained to maintain compliance to truck lift truck rating capability. 4.) This may be you best solution - tire companies make tires in a higher durometer (hardness rating) The harder the tire the rougher the ride & higher the price.
The squeegee effect when turning tight will cause faster wear & cracking. When a truck is operated empty ~60-65% of the gross vehicle weight is being carried by the steering tires (they are smaller than the front ones & generally last 1/2 as long or less if a lot of tight turning is done with the truck sitting still- operating training might help kinda' like teaching a teenager not to burn rubber with the families station wagon.
My suggestion contact your local Yale dealer (service department) and they can (or should be able to) answer or provide info all these items.

My other thought is you seem to indicate your fleet of 5K handles light loads the majority of time and only occasionally heavier loads. This means your tires are seeing constant heavy loading. to me. In the future you way want to step down in lift capacity to a 3K or 4K (long wheel base unit, not the a short wheel base) for the majority of you fleet & only have 1 or 2 5K units.
One thing you failed to provide us is the floor conditions and the status of the floors at the expansion joints. It get cold up there and floor foundation shift from freeze thaw cycle take there tolls on concrete
Hope this helps, ask a question if you need information.