I'd not try Mobil 1. I tried applying Break*Free with my fingers many years ago when sizing .223s and had not only my first ripped off extractor rim, but my first die ruined in the course of trying to remove the stuck case.
I was wanting less gummy friction than the traditional RCBS roll-on-the-stamppad stuff I has used up to that time, and was tickled pink with how slick the Break*Free was working... Because both the stuff I used and Mobil 1 are synthetic lubes, I would expect them to have similar film strengths under pressure.
I believe that part of the problem is that if you get a bare spot on the CASE, the thinner lube is less likely to forgive you that error with a nice residual film inside the DIE from the last case sized.