For the quick and cheap solution, I'd do something similar to how this battery is held down
4 segements of 3mm steel across each leg which have been drilled on each end. Two long 5/8" screws on each side of the steel and into the platform. A fair bit of the screw will stick out so make sure it gets a good bite on your platform.
Filing your cuts on the steel is a good idea. Washers on everything, screw in just enough to hold it in place, male sure the plates aren't under huge amount of stress. Something between the rack and the steel won't hurt.
Get at least 3mm steel. Eg:
Hacksaw will do the job cutting.
Make a bracket (you just need to add a vice and make some measurements to the above) and sink the platform where you screw the bracket in if you want a neater solution