Joe, the bending of forks should not become an issue if the load is within the rating of the fork. The answer of increasing the cross section will increase the capacity of the forks. The relationship is 1/4 inch in thickness equals about the same as 1 inch in width. BUT...
It sounds to me that the real problem is you are using mass produced forks made from rolled flat bar. These forks, sold by almost all fork suppliers here in the US, are NOT heat treated fully and they are NOT fully forged. They are hardened only at the bend. Heat treating fully to the correct hardness spec over the entire fork will reduce the flex of the fork dramatically.
If you use a fully forged, fully heat treated fork, such as the ZYatWork brand sold by Fork-Co USA and Trading Point Products, my bet is you will not encounter the flex/springing problem using the same fork you currently use. That is, unless you are now using a fork that is very much too thin and under capacity as it is.
You won't find this type of fork from the sellers who deliver flat bar or plate plate forks. They don't hammer forge flat bars. ZYatWork hammer forges round bar alloys to make the forks...100% forged. You can reach them in the USA at 281-648-2723.