You have an excellent instrument on which to learn some repair techniques. It is a decent instrument that is likely to improve from your efforts.
You are correct in looking at the facings. They can be a major source of leaks. Replacing pads won't do any good if the facings are not in proper condition.
Rough tone hole facings are a common problem with bassoons. This can happen just as a matter of time. Facings are commonly varnished in one way or another and it is probable that the varnish has chipped away leaving an uneven surface. The thick brittle varnish used by many German makers is especially prone to this problem.
There are several ways to smooth tone hole facings. Sand paper can work but it can also damage the surrounding finished surface. I prefer a straight bladed knife. Use it to scrape the surface smooth. If you can scrape a reed you can probably learn to scrape facings. As much as possible try to move with the grain. Try to stay aware of how the wood wants to be worked. If you try to fight the wood you will lose. There is no single blade angle that works all the way around a facing. You'll find that you can readily shape the surface of the facing. If, at the same time, you apply super glue sparingly with the knife blade you will find that the glue can seal and help smooth the facing. Don't do too much at once. Even instant glues need time to dry. You'll need to scrape the buildup off of the blade frequently. With some practice you'll find that you can smooth and seal the tone hole facings quite nicely.
Take care not to work the rim of the tone hole too much. You want to leave that alone as much as possible.
This is a labor intensive job that often needs to be done when pads are replaced. Specialist shops know to check the facing surfaces and correct them using their favorite methods. Other shops may never give the facings the consideration they need.
Let me emphasize that there are numerous methods for renewing the surfaces of tone hole facings. I'm describing just one method that makes use of a tool you already have in your reed kit plus readily available super glue.