Lots of great ideas here...
My initial suggestion was going to be not to concentrate on 'perfect' for this one. Which would be ok with kids hand prints. But reading backwards before posting my comments (better idea is to read forward
) I like your plan to modify the quilt you posted. I think it's very doable in the time limit you set. No seam matching and just the applique. If you have a machine for embroidery, that would help. If not, do you know someone who does?
Good luck - post pictures when you can