I have seen this done as a 'rectangular' quilt in a book I have somewhere. Instead of a square in the middle it was longer than wide so that the quilt did not turn out to be a square. It's actually quite lovely. My advise would be go for it but I would think you might want your logs to be a wee bit larger than 2.5" wide.
I've also seen it done as placemats (again using rectangle). This time I think the strips were cut at 1.5".
So sorry about your leg ... do you have any 'hand work' to keep you occupied?