Hi everyone.,
Letting you all know how this turned out. I actually read all of the replies. Several mentioned cornstarch, and one, by Northmount mention "Floor-dry". So in addition to getting more cornstarch at the grocery store, I went to the hardware store and got something called "Oil-Dri", which comes in a 10lb bag for $4, and look a lot like kitty litter. I put half of the straps in cornstarch and the other half were buried in a container of the Oil-Dri, for almost a week.
All of them came out less oily that when they started, but the ones in the Oil-Dry were noticeably lighter. So, I put the ones that had been in the cornstarch in the Oil-Dri for a week That might have been too much. I had to compare them with a scrap of the original to make sure that I had not completely dried them out. I re-oiled them a little, but this time NOT by immersion. I just put a few drops on a rag and wiped down just the shiny side. I could see the new layer of oil quickly get absorbed into the leather. I did that few times.
So here is what they looked like then. Lying across is a sample scrap of untreated leather for comparison.
Not shown are some smaller pieces that I put only in cornstarch and never in the oil-dri.
Here is the final product after assembling them and fastening the rivets:
Thanks everyone!
For anyone else with the same issue, remember that cornstarch works okay, but oil-absorbent such as Oil-Dri works much faster.