Purlin Span?

I am renovating a barn like building which has a king truss roof with a single purlin. The roof is old, and the purlins are deflecting a little. I have done a rough calculation and the rafters are over sized, but the purlins (3x9) should really only span 3.4m, instead they are spanning 5.3m.
Adding extra purlins will make the roof unsightly, and be a pain so i want to avoid this.
Any thoughts about adding collars across the rafters to help the suffering purlins? Has any one had this problem before, if so, how did you solve it?

Thanks for any ideas!

sorry…but we are roofers not carpenters or engineers.