For the record...the most often used (by writeups anyway) method for getting the outer race out of the hub (cuz, like you say, you can't reach it when the bearing is destroyed) is to tag a bit of welding rod to the race. Generally, when it cools it will come out easily. If not, the welded bit gives you purchase to tap it out from the other end.
RE: taking time over not screwing stuff up.
Good job!! Too often there's enough time to do it twice, but not enough time to do it right the first time. (the second time usually ends up costing you more, too! ;) )