Note that you would have to power down the modem and the Roku, connect the Roku to the modem, power up the modem and allow it to complete the boot process prior to powering up the Roku and testing.
Yes, I've spoken to six Roku support reps and they've walked me through this process each time (although they contradict themselves -- and the Netflix reps -- in other ways). Unfortunately, my Roku is in the basement and the router in my office above it. No easy way to connect the Roku directly without drilling through the floor, something I'd prefer to avoid. Any help with the proper QOS or wireless settings would be gratefully appreciated. I don't know much about that stuff, but a setting adjustment makes more sense to me than a router replacement.
I think there is some confusion as you say Roku support already walked you through this process six times already but I was referring specifically to the process you should follow when connecting your Roku directly to your modem....if you have done that six times already and the problem has persisted then my suggestion is irrelevant.
I was just putting forth what I would do were I in your situation....eliminate the router, even if only temporarily, to see if the problem went away or not......determining from the results if the router was indeed the problem. If the problem goes away then you can start digging around for help specific to that model router and the problem you are having.