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You could do it either way, or have it set up to have the hitch in, take it loose, then bolt it back in when done so as to get under the hitch coated too. They can mask the hitch so it won't get coated where it needs to be loose, so it basically depends on how you want to do it. The only reason I can say without a doubt the hitch would need to be done first is that the drilling and cutting that is involved to mount it will damage the coating a bit, and can make it more difficult to do perhaps.
i just got my B&W turnover put in and i have had my spray in liner for a couple of months now it looks just fine they cut the liner the same time as the bed i vote for liner first.
I did. He said it made no difference to him. Ball first means the liner material covers up any edges from the install. LineX first means they simply cut through it during install.
I did the hitch first and Line-X after. Looks great and everything is coated. As you said, when not in use, it is completely un-noticed. Glad I did it this way.