I don't know about FMQ but consew are great machines. I used to use one. Great for straight line sewing.
I would think if you can cover or drop the feed dogs and adjust stitch length to zero and have a darning foot you can do this. Simple, right !
I just watched a tute where on one machine that the feed dogs didn't drop the teacher covered the whole sewing surface with plastic cling wrap (nice and tight around the edges so as not to shift) and this simple tip allowed her to move the fabric without having the feed dogs interfer. Isn't that cool!
peace