"Modern medicine relies on petroleum, particularly to transport patients, staff, and supplies"
That part is largely 'solved' problem and the rollout of those solutions over the next 30 years will probably be significant. As far as plastics and pharmaceuticals are concerned the paper puts it at "an estimated 0.2% of petroleum used in the United States was for medical plastics"
As for plastics in general the current number seems to be in the 6-10% range globally depending on who you ask. With a combination of reducing, recycling and misc. technology improvements I'm sure we can get that down further in the next 20-30 years. And much of that oil can probably come from sources other than pumping it out of the ground.
So on the whole I think winding down the petroleum industry as we know it today over the next 30 years to a fraction of what it is today (no one is seriously suggesting 100% shutdown) is absolutely doable, from a technology point of view. The reasons why it won't happen are political.