Wald "Heavy Duty" delivery basket implies strong legs, mine has thousands of miles, not one sign of stress on my "non-suspension" forks. I've mounted mine to the forks, cut off the axle mount holes at the very bottom of the legs.
I have seen black rubber "egg carton" packaging, similar to the foam type used for sleeping mats, which could be layered at the bottom of the basket and act as a shock absorber.
Or a vinyl or rubber sandwich, with bubble wrap in the center, would get the same effect. A thin bean bag full of foam peanuts might work. Even styrafoam confetti could be made from egg cartons, to lift the batteries off the bottom of the basket.
Lawn mowers use the strong black rubber bungie cords to hold the battery in place, and 3-4 of those stronger type could hold the batteries down.
Longer bolts could be substituted on the bottom of the basket, where it attaches to the legs, and rubber washers could eliminate some of the bounce.
Those are ways to do it for the least amount of $$$.