Tedious solution...
Really "out of the box" idea here so don't try it unless you're daring
How much time do you have to build this? a week? a month? a few months?
If the last one then you might try a really tedious but versatile solution: You electroform the copper pad structures onto the PCB.
Essentially you "grow" the pads right on the PCB atom by atom.
The idea is you get your PCB and etch the traces as usual but also include large "pads" of copper that will serve as the heavy current traces. Then you cover up all of the traces you want to keep "normal" with waterproof tape leaving the high current traces alone. You then fix a wax mold (with plenty of solution access holes) onto the PCB to make the traces grow into the mold in the proper shape, this is to prevent them from growing toward each other and shorting out. Then you connect it to the cathode of the high current low voltage (10-50 amps at 0.3v) power supply and dip the PCB/wax mold into the copper plating solution and let the copper ions plate onto the exposed sections of PCB.
Takes some time to get a good deposit and you need to carefully control the solution chemistry to get high conductivity of the final product.
At the end you take it out, break off the wax and remove the tape and after some sanding and buffing you'll have a PCB with a huge THICK copper pads that could take a few hundred amps of current (or more, i never tested the upper limit).
The amount of copper you'll add on can be a millimeter or a couple of centimeters thick depending on how long you leave it in the solution (the longer the thicker)
The other traces that were covered in tape are normal so you can solder your control components.
The thick copper is strong and drillable so you can drill holes for the bolts or clamps you'll connect the cables with.
Very tedious process to learn and do (your first ten tries WILL look like crap, but you'll get better), but in the end you can make things that can handle gargantuan currents.
Also a fair bit expensive if you're just starting off.
I first used this process for the unrelated task of making copper plaques for ornamental purposes. Then i applied it to making an extra-thick copper heatsink/conductor pad for a switch mode power supply i was building.
I tested the 5 millimeter thick pad (which covered about 6 square inches) with a current of 100 amps, didn't even get warm. (i didn't test further for fear i might cause something else in the circuit to explode...)
it was thick enough that i could securely drill and screw on a rather large diode and mosfet combination that had screw connections for its leads.
the copper is fully solderable if you sand it down smooth enough. (i didn't bother since i wanted to able to screw and unscrew replacement mosfets everytime it blew)
for more information look up "copper electroplating" on the internet. the process is not used for electroforming commercially (metal casting is faster, simpler and WAY cheaper) but copper plating is used extensively by the electronics industry for through-hole connecting.
....btw the same skills for electroplating copper also work for chrome plating your own car parts, restoring them to showroom finish.... (HINT HINT)
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If you don't have the time to do something this complicated then i would suggest just buying some copper stock sheets from ebay or onlinemetals.com. Cutting them to shape, sanding them down, and soldering them over the traces you have on your PCB. Faster, simpler, and cheaper.
or do what JustDIY said and get some different components that use screw connections. Buy a copper plates that's 1/4" thick, drill holes and screw the components in. Your control electronics only need little 10 miliamp wires for their connections.