I have a similar setup and put some 1 X 4 between supports on the slope to prevent that. For me it prevented puddling, but in your case it will give it more support. Extra piece of mind
Funny, I just put a new cover on top and was telling my wife it would be nice to add a few more rafters... I was thinking emt conduit.
My tent is 18'x20' so the roof supports are pretty long.
