From my understanding, most fossil formation has to do with remineralization, movement of minerals (ossification is just bones, right?) etc. You can find Revolutionary War and Civil War relics in rivers with minor mineralization already taken place. If their is enough iron or calcium in the water it can happen under medium to low pressure.

My guess is that under high pressure, with sufficent mineral concentration, fossilization could happen in hours, days or months at the most.......under the right conditions.

Osmosis and such doesnt care if the creature was alive 2 hours ago....as soon as the cell walls start to break and leak, in come the minerals and out flow the organics.

I read a couple articles about this in college, but doubt if I still have (or could find where) the photocopies.