Could just be a symptom of worn shock absorbers, but what is the offset of your wheels and what size tires are you using?
As for the strut brace, the TRD 4-point strut brace is near impossible to find nowadays. You can however get an 8th Gen Corolla TRD 2-point strut brace and fit it with a small amount of modification, but I'd recommend using an OEM 3-point strut brace. These came on JDM GT Apex Levins, the AE101 Corolla GT, Sprinter GT and a couple of others. I think they also came on some USDM models too, but they may have been 6th Gen's. It bolts to the firewall and provides the best rigidity there is.
I've got a spare one sitting in my garage. Here's a photo of the one on my car: