PCB Trace inductance
What are your specs for resistance of the copper?  If you can meet the resistance specs the inductance problem WILL BE REDUCED to the same range of impedance as the resistance for flat copper.

If the Length, l, to diameter, d, ratio is known, you can calculate the Inductance, L , series resistance , Rs and the aspect ratio l/d is related to Q = L/Rs for a given conductor material.

Let's consider the impedance for copper at 1 MHz.  


aspect ratio,      =       l/d =   5   10  125  1250  12,500
Impedance quality =  Q  = L/Rs  2.6  4    8    12      16
where Impedance, Z= ZL + ZR 


For flat copper tracks the aspect ratio is quite different and lower Q but you will need very thick copper to reduce the ohmic loss @ 200 A.

I would suggest you use thick braided wire from the board edge and make the copper loss and inductance less than the Ron of your switches and not rely on copper traces. Thick tracks would make the cost of etched copper loss too high {unless you consider solid busbars added to board..}