is 100% right. The collet nut turns counter clockwise to loosen it. It is the normal lefty-loosy arrangement.
The collet nut should not scrape the router bit as you loosen it, even though the router bit is flush tight. The collet nut is actually a sleeve around the inner parts (the "collet"). There is an inner ring on the collet nut that engages with matching slots on the inner collet parts as the collet nut is unscrewed. As you unscrew the collet nut, it will lift the inner collet parts out, and the router bit will lift with them. (Note: The router bit may be stuck in the collet itself, but that's a separate problem to deal with after you get the collet out of the router.)
-> If your crescent wrenches can't tighten and stay tight around a nut, then why do you still own them?
I think you need a well-fitted wrench with thick jaws that will stay tight around the collet nut. If you can't swing that, could you use your two best wrenches in tandem to increase the contact surface area (taped together, perhaps)? Will they fit?
As others suggested, I would lubricate the collet nut and threads in the collet area with liquid wrench or another penetrating lubricant. Leave it soak for a day, maybe turn it and lubricate it again, etc. ...
With the collet lock button depressed to hold the motor shaft in place, try gentle tapping on the end of the wrench with a brass hammer (or metal hammer, if nothing else) to break up the rust inside the collet nut. Gentle. Tapping. Not hard hammering. You don't want to damage the bearings or bend the shaft (eek!).
Consider applying warmth (not serious heat) to the collet nut, then try again.
Good luck. Keep us informed.