The satchel was finally completely dry when I checked on it today so I applied the first coat of Neat's foot oil that I am using as a finish to it. I was happy to see that it did even out to color of the satchel like I had hoped it would. I also discovered something interesting, it doesn't smell strongly of vinegar like the other pieces I've used the iron oxide dye on. (I make the iron oxide by leaving steel wool to dissolve in vinegar and it definitely imparts a strong smell to the pieces I've used it on.). I'm guessing that soaking the pieces to make them easier to sew twice rinsed out the vinegar. On the second soaking it also appears to have leached some of the tannin and iron out of the leather because the water was black after a few hours of soaking.
I'll check on it tomorrow to see if it needs another coat of the oil and then all I have to do is cut out the strap, get it dyed, finish it with the Neat's foot oil and then lace it on. That's something I can easily do this weekend.