A fascinating experiment, Curer. I only have a couple of comments. Firstly, I think it would have been fairly common practice to have a slave massage the oil in. We need you to try rubbing the oil into your skin before scraping to see how much residue is left. Secondly, I would persist in finding something metallic, curved, and about the right size. Different sized strigils were used on different body areas, so size would seem to matter. Lastly, post-scrape, we need you to hop into a hot bath, then a cold one. This may have the effect of getting rid of the last oil vestiges. Please let us know how you get on.
The other thing is that I'm pretty certain that the whole acne/oily skin connection is a myth. Acne is caused by (typically) adolescent hormonal imbalances/excesses, and so all these facial rubs will do little more than attempt to clean out your blocked pores offering temporary relief. So I wouldn't use that as any kind of success criterium.