Reddit mentions of iNee Natural Linen Fabric for Needle Embroidery, Embroidery Fabric Linen 20 x 62 inches,(Pure White)

Both those pieces are great, even the first one unfinished. A couple things I can think of to try that might help: maybe trace the edge of the felt with some kind of ravel stopper like this https://www.amazon.com/Dritz-674-Liquid-Sealant-0-75-Ounce/dp/B0019KBWA2 like maybe just put it on the cut edge, or a little way in on the under side of the fabric? It'll be hard to stitch through so a thin line to keep the edge clean but you'd kind of loop the stitch over it, if that makes sense?
Second, you might use a base fabric with a wider weave, like looser space between thread (https://www.amazon.com/gp/product/B0771RF2QR though you can probably find something halfway between this and what you're showing in the second pic). Then you might try separating out the floss so you're only using 2 or three strands instead of all six, and use a smaller, VERY sharp needle (look for needs called 'sharps' these might be small but something like this https://www.amazon.com/Clover-Gold-Eye-Sharp-10/dp/B001K53MBS) . This will put a smaller, neater hole in the felt so there's less fraying. And the looser weave fabric means that even with paint you won't have to press as hard to get it through all the layers.
I hope some of this advice ends up useful. Good luck! I can't wait to see it finished.