I'm not sure what your machine is, but an older (mechanical/metal) machine should sew this. I have a 401J and it would handle it. I can't say re the newer electronic ones because I haven't tried to sew very heavy materials.
It might be cheaper to buy an older machine vs renting on upholstery machine if you could audition your fabrics on the machine.
(Guessing that this isn't the first or last project you may be helping with???)