surprised nobody mentioned weight transfer, a super well known braking effect.
if the operator brakes as the teeter happens, the rear is unloaded and "weight" is transferred quite significantly forward (this is not actually transferring weight obviously, what you have is a combination of the center of gravity being higher than the point of resistance of the forward inertia, creating a lever arm, I think. if I got that wrong, please correct IF you can explain that better!),
the rear of the platform is unloaded right as the front hits the stops, and it is still traveling up. obviously you would need some forward velocity but I think it would be human nature to hit the brakes just as the teeter happens, and with reaction time and mechanical delays, it could time the unloading perfectly to maximize shock load in the up direction.
as to the original "design" I too have some questions about the engineering..? from the photo it looks like the stub axles are particularly flexibly mounted (although someone else posted that they were subsequently welded to something at the inside end?) and cobbled up with bar and pipe. I hope the bar isn't high carbon, or its going to break at that weld. better to have it sticking out of a snug fitting block of 1" min. thick steel, with the weld on the backside only, putting the HAZ outside the highly stressed area.
Junkyard ( excuse me,recycling center!) trailer parts are actually designed and engineered for this function, made of decent quality steel, and are pennies on the dollar, why not use them?
an "I" beam which is actually a "W section" usually, (12 X 22 is a W section) is particularly bad at resisting torsional load, so particularly unsuited as an axle, although at the speed of rotation here probably not really a factor.
as to the retrofit, I see no particular reason to recreate the original form of the pillow block. I'd probably bore it out of rectangle bar on the lathe and bandsaw it to a simple form, but I don't know what your shop has for a vertical bandsaw. looks like it will hold, if you have some actual support for those little stub axles. good luck and keep us updated!