I use a 48" Dewey coated .260 rod for my 338s and my 510AM. I think they make a longer one as well, check with Sinclair.
What are using a 52" rod for? I have a 510 AM with a 40" barrel and my 48" rod works fine.
One suggestion you might try....... Rather than a jag as you mentioned, I use a nylon brush to hold my patches. Take a .30 cal NYLON brush and 2 12 ga shotgun patches. Start at corner of the patches and wrap the patches around the brush. I have found this works well for 338 cal, 1 patch works for 30 cal, and 3 patches work for 45 cal. For my 50 I use a 45 cal brush and 1 patch.
The two patches on the 338 cal will hold lots of solvent and provide a long wiping surface. They fit snugly but not so tight that you will need a hammer to get through the bore.