For me there were 2 reasons for a false bottom:
1. to get the bag off of the bottom so as not to melt it.
2. it creates a temp buffer that keeps you from overheating the bottom portion of the mash where it is closer to the heat source.
I recommend just making your own false bottom. A cake pan that roughly fits your kettle with a dozen or so holes drilled in it. Then create some feet to elevate it off of the bottom of the kettle. I used SS bolts through the pan. I found the cake pans work especially well because of the raised sides creating a sort of 'cradle' to hold the bag. Your less likely to have the bag mashed down in between the false bottom and side of the kettle. This worked well for me when I was a BIAB guy. 2 cake pans bottom to bottom work well also.
Having said all that... I almost never do step mashes so my all grain cooler tun has, for me made mashing easier with better temperature control. Once you learn your tuns specific heat and dead space, doughing in to your target mash temp is pretty easy.