While the wait time to rent a machine may be long (I didn't even know Denver had this,) Denver also has the ideaLAB maker spaces at five branches, all of which are equipped with sewing machines to just drop in and use.
Some ideaLAB locations (like my local one) have fancy machines like embroidery, quilting, and industrial sewing machines. There's also lots of other tools, from basic hand tools to laser cutters and 3d printers (again, location dependent.) There's always staff on hand to help during open lab hours. All free to use. Really an impressive system that I use frequently.