I've figured out a solution! (At least for my issue, it's very similar to this)
If you 'route' your inputs through vJoy (for lack of a better term) it bypasses whatever processes are causing the delay and allows the joysticks to work perfectly (Saitech's X-56 HOTAS, in my case).
You can find vJoy here - http://vjoystick.sourceforge.net/
Then, after installing it and UJR (vJoy will have a link to it), bind any controls that have input lag to the controls in vJoy. Then, bind the controls in KSP to the vJoy controls (NOT the controls on your actual stick). You will have to use the quickbind feature in vJoy to do this, just read the blurb about quickbind at the bottom of the main UI for how to do it.
After doing this, it should work perfectly!
Good luck!
(Sorry for any confusing writing or explanations, it's 3AM for me and I just figured this out. I'll try to remember to come back and check this tomorrow.)