A small Jerry Fisher scraper or barrel bedding tool, the type with interchangeable discs will make short work out of the grasping grooves.
Start from the other end and as you get towards the end of the groove let up pressure and they'll come right up to a nice taper where they end.
Then turn it around and scrape the other way. Depth and width is determined by how hard you press initially.
Go easy at first to avoid a run off/establish initial cut. You'll not need sandpaper in groove bottom and transition to the stock wall will be sharp as a tack.
Project is coming along nicely-Looks great!