Going to work just fine, however In looking at the tool marks in those barrels common on modern rifled shotguns, I think I'd do one of two things. I'd get a mould casting a slug and fire about 50 fire lapping rounds through it - or - lead lap it with similar compounds.
You can bring up several fire lapping 'kits' and/or instructions if needed. Pure lead bullets are used.

I've done this myself with several rifles and came away a VERY happy camper - every single time.

The fire lapping and/or lead lapping will remove or smooth the crosswise reamer marks to lengthwise with the barrel and eliminate or reduce immensely the fouling you'll get, otherwise.

Just a suggestion.