So, let it soak in naval jelly for about 90 minutes (Tom in CA's go to solution). Unfortunately, the naval jelly leaves a pinkish hue on everything I've cleaned it with.
Then, gave it a good rub down with Braso for about 3-5 minutes. That took about half of the pink hue away.
Finally, rubbed it with 0000 steel wool. I think this is the closest to original coloring I've ever achieved.
After all that, I showed it to my wife along with one that hadn't been cleaned at all and she said she preferred the uncleaned version with the reddish/brown rusty patina.

Thoughts?