I'm SWAG'ing that the three Edcor trannies would weigh about 26 pounds, and the 3 mm thick panel should be plenty strong enough for that. The trannies will be closer to the rear edge, so the Hammond chassis base will help support the weight. The rest of the chassis mounted parts, circuit board, etc shouldn't add too much additional weight, and that would be more or less evenly distributed across the plate's surface.
If you have an unused / spare 3mm plate, try supporting it by the two ends (on 2X4s) , and stack up some weight onto the middle and see what, if any flexing may occur.
In a couple of cases where I had a regular (read that as thin and flimsy) aluminum or steel chassis with a heavy iron load, I used a 1/2 or 2/4 inch aluminum angle bracket under the chasis, with the front-most mounting holes of the trannies all drilled in a straight line, and put the (matching-drilled) angle brace under these, and thechassis load bearing capability was greatly increased.
This would take a relatively flimsy thin chassis top and make it nearly as rigid as a steel plate... With a 3mm plate, it could probably hold up a hundred pounds
without noticeable flexing.
/ed B