Yes this is a dilema. Let's go over all the options so you can make an educated decision. First, it is unlikely that the intact unit would block off an oil passage. The size only would make this unlikely. I is a very remote possibility. Second, the card board is pretty soft, so the only real problem you may have is if it gets chewed up in the valve train and the smaller pieces block an oil passage. I doubt this would happen and an oil change would take care of most of these particles. Not a best practice to do this if you can avoid it. I also doubt you have to remove the head to get to this cardboard. Removing the valve cover should be sufficient annd is pretty easy. You mentioned a bad back, but very little lifting is involved in this and easy a very easy job. If bending over is the issue, try driving the car onto ramps first! Make sure you set the brake and place a chock behind the rear wheel.
Considering the cost of engine problems, even though remote, I would not let the need to drive be the governing factor. Possibly rent a car for a few days, or bum a ride, take a taxi, etc, and deal with the valve cover in a more liesurely fashion and know you have fixed it right. The tow and pay a mechanic route is also an option, but obviously a little more expensive and less satisfying.
87 300TD, 160,000 miles
72 280SEL 4.5, 250,000 miles