Kitchen towels with rancid grease smell

I hope that someone here has an answer for me. I have "flour sack" kitchen towels and I love the job they do drying dishes and drying my hands. HOWEVER, bless his heart, DH seems to think that they're napkins/mops/Kleenexes/stove cleaners, etc. I've suggested that there are other sponges and scrubbers and, gasp, actual Kleenexes to take care of those jobs and he gets that look that a cocker spaniel gets when you give him a command he doesn't understand. Head cocked over, ears pricked, looks at you like you're speaking Greek...

My problem is that since we do laundry once a week (only 2 of us, trying to save energy by not doing small loads) these towels sit with various types of grease and oil on them for days and even if they come out of the dryer smelling clean after a few days in the cupboard they reek of rancid grease. Has anyone found anything that will get rid of the smell? I've tried baking soda to no avail, and I'm not sure what else to try. Rancid fat is one of those smells that I really loathe, so I'm trying to type with my fingers crossed in hopes that someone here will have a solution for me. I've gotten to the point where I'm wondering if I need to get a "towel pail," like my mother back in the day of cloth diapers had a "diaper pail." Hmmm... That might work, if only I knew what to put in the water!