When I had my frame apart, I should have done a little more research and done some bracing/boxing on it. When I put it on jack stands at either end, it sags in the middle a fair amount, more than I'd like to admit
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I'm doing the same things that you are looking to do with yours but without the bracing and boxing. If you plan to have a lot of fun with it whether it's on twisty roads or in autocross events, I wouldn't hesitate to make it stiffer. My next frame will definitely have more thought put in to making it work for autocross and track nights.