John Paul Sanborn
Above average climber
try semi chisel or skip chain. the semi chisel is suppose stay sharp longer in dirty wood. Skip chain has less teeth so it take shorter time to sharpen. Otherwise try to keep itt out of the dirt
This is what i would do in your setting, the cost of sharpening carbide would eat you alive. Semi-chisel is rounded and does not dull as fast as the pointy full-chisel. Also, rocks will break carbide cutters too, and the links are pricey.
Get a stiff brush and hatchet and take a little time cleaning up the inclusions on your stumps.
Lastly, buy bulk from a mail-order shop, like our sponsor Bailey's. It will be cheaper per unit, and changing out the chain can be faster then trying to regrind several cutters in the field. Then you can take the time to do it right on a vise, in the shop. Time is money when on the job-site, it is just time when you have a choice between watching Jeopardy and working on tools.