I hunted on a leftover cow tag last year, in an area made up of about 5 NW Colorado units. It was a good year to do that since 10" of snow fell in my "usual" hunting spot the week before opening day. A lot of elk moved down to lower elevations, and if I didn't have all those units to choose from, I'm not sure what I would have done. But we made the adjustment and moved about 80 miles to some public land that was around 6K feet (I had previously hunted between 9-10K feet) and found plenty of elk, even in mid-October.
I'm not sure which units offer OTC cow tags, but there were literally hundreds of leftover cow tags last year that weren't hard to get online.
BTW, I've been hunting cow elk for the past 3 seasons and have yet to kill one. During that time, I've had multiple point-blank encounters with bulls, some as big as 6x6, but couldn't shoot them. Maybe it's just my luck, but this year I'm probably going for an either sex or just a bull tag. Those cows can be darn tough when there are 30 pairs of eyeballs guarding the herd.