All you really need is a little plastic thing of needles ($1), some pins ($1), thread (varies but even good cotton thread isn’t that much), scissors (where you might actually consider investing a little - do not use these scissors for anything else, and consider a rotary cutter if you really get into it), and fabric.
Fabric might seem like the pricey part of the equation, but consider how much a thrift store is going to charge you for a duvet or a pile of t-shirts! I have something like 30 t-shirts I spent maybe $5 on several months ago, and I’ve been working through that pile for a while.
You can turn a t-shirt into a pillow, a reusable bag, use the scraps to patch clothing, make dolls, quilts… The bits that get to be so small to be unusable for a scrap quilt you can use to stuff things.
It takes a lot of time compared to machine sewing, but it’s an activity that can be done while watching a tv show.
Honestly, I have no clue what thimbles are for. But I realized at some point this year that instead of using some hard surface to push my needle through assy material and/or hurt my finger pressing too much, I can just… Use a metal thing that sits on the right spot.
Also I know this sounds weird but go to a shop and try them on. It’s weird how much a good fit helps.
The cutting out would probably be the way to go. I mean you could flap it, so it stays connected to the right spot, maybe it’s time for you to be brave and risk it. Especially since you have a sewing machine! That means the seam can turn out quite nice when put back in place. Anyway, good luck and updates are appreciated!