Getting the Travis industries large flush wood insert installed soon. I need to get electric to the back of the firebox for the blower. My ash dump clean out is in the basement and the ash dump is in the back of the firebox.
Assuming the bsmt is where your breaker box is, you could drill right into your chimney (above the ash cleanout) and run shielded cable up through the ash dump.
Read the code in your area, ESPECIALLY if you need to pull a permit, and don't hesitate to call the city people, they like giving advice, it makes the permitting/inspection go better for everyone. Where I'm at, i could have done an outlet (for a plug), but only if it is in the same room. No plug running to the basement or another room. So, mine's hard-wired, with a switch just in case.