illinois

Remember those boxes that checks used to come in? Wonderful!! It's small enough to be portable and actually can hold "a lot" of stuff. It's easy to put on top of the quilt as you move along or to put next to your chair on a table or the chair. The box I am using holds a magnetic pin/needle holder, thread, thread clippers, a 6 inch ruler, mechanical pencil, thimble, a pkg of extra needles. Love it. All of the essentials are together in one place and it's not in the way--if it is, it's easy to move, yet accessible. Other than a template, what else do you need besides needle, thread and a thimble?
Now that I am rereading your post, you comment that your frame sits at an angle. That's probably the problem with having something such as any container placed directly on the quilt. Depending on how taut you have the quilt, even my suggestion might not work. Yes, something to sit beside you will be the best. I'd want an open container so I could easily see what I'm needing for the next step such as rethreading the needle.