I know that Mossberg is making cantilever scope mount fully rifled barrels for the 12GA 870. Not sure if they are making them for the 20 though. If not, I would opt for the Remington barrel. It is the most expensive option but at least you should have it sooner rather than later. Cancel the order for the Hastings and look elsewhere.
FWIW, I have a Hastings barrel just like you ordered but for my 870 12GA and it shoots great. I bought it on sale after the hunting season a couple years ago for $150.00. The ironic thing was that I sold my stock 870 smooth bore barrel with a rifled choke for $155.00 on E-Bay so the replacement barrel cost me nothing...