Multiple reamer steps can result in cumulative offset, so I wouldn't recommend it as a first approach. I've never been able to open a smooth round hole more than a couple or three thousandths with one without some centerline offset or some unintended beagling occurring. What you could do, though, is follow BillM's suggestion, and if the resulting counterbore doesn't shoot well and/or throws fliers and shows copper wipings, then use chucking reamers to widen it further until it works.
Another approach would be to call Dave Manson (Manson Reamers) and ask if he can make you a narrower 90° cutter for the Brownell tool and find out if the price is something you can tolerate. The reason I suggest 90° is that even if it gets a little off-center, the crown edge gets a uniform angle all around.