Quilting can be a great stress releaver. You mentioned using pre-cuts and I think that would be a great idea. I would suggest visiting your LQS and if you can afford to buy the pre-cuts they may have several simple and quick quilt ideas. With the new pre-cuts of charms, layers, jelly rolls, and turnovers there's sure to be quilt idea to find.
Many times LQS have quilt kits already put together. These sometime require extra cutting of the fabric. You might ask though if they would be willing to complete all of the cutting requirements for you. You may an additional charge for this.
If you have a quilting buddy you might be able to enlist their help for cutting while you're on the meds. If you're in a guilt group there may be someone who would be willing to do all of your cutting. You could reward them with fabric.
These types of needs are the reasons that quilting bees and our current clubs were formed. If you're in guilting group this should be a topic for discussion. If you're having sewing issues there may be others as well. Maybe you could have some group sew-ins to help each.
Good luck with your quilt project.
Pam M