Use an oscillating multi tool to cut out the oil soaked area.
The tool is 20-30 at harbor freight if you have one around and they come with some blades/bits.
The replacements blades and bits cost more than the tool in the long run and my harbor freight tool vibrator doesn't get used a lot but it is very usefull for what it was designed to do and is there when need to trim/sand corners that I cut a touch to long and can't get the board out with out messing it up?
Will work for you.
I Agree with even the best of the best products not sticking to anything with oil on it.
The only wood construction I do is at home but I have had to tear up concrete in brand new construction where my threading machine sit.
It didn't look that bad when I left but the epoxy flooring didn't stick and my company had to pay to fix it. Because of the oil on/in the concrete.
Don't know the names of companies but they do make a commercial rubber flooring in 2'x2' squares or variable sizes that don't really stand for 10-yrs but do good (left over brand new ) in my house as chair pads at the computer desk and in my boys rooms at there study desk.