Happily, there are tools designed for such problems.
And here we have the June Tailor Quilter's Cut 'n' Press, which has a small cutting mat on one side and a pressing surface on the other. It's a baby ironing board! (I don't know nothin' about ironing no babies, so hush; you know what I mean.)
Now we just need some steam. The Steamfast travel and crafting iron should be just the ticket. Let's take it for a spin.
Yep, works great! It gets quite hot, and produces audible and visible steam. That fusible is well-fused.
I crawled into bed with some more crochet cotton and a loooooong sashiko needle. This was the result. I think I'm going to make a little zipper bag out of it. That seems to be my default. Everyone likes a little zipper bag, right?