Although I sold my HE5000 in March, I did have it last year and did "summerize" mine. I'll tell you what "I" did but that doesn't mean it is right.
First off, why did you drain it? I was/am under the impression that doing that will premote rust. Leaving the water in will keep it from rusting.....
I cleaned all the ashes out and used my shop vac to clean fire box and refactor chamber of all ashes......btw, shop vac filters do not fare well with hot embers and good air flow
so, make sure it is completely cold...unless you need a new filter anyway.
I scraped the inside walls and top with your normal type scraper clamped to a wooden handle to reach in. I did not go crazy, just scraped all the loose stuff. Make sure you get the 2 back lower corners well, this seems to be the "gathering" spot for build up. I then sprayed a "cosmoline" type of protective coat, similar to what is on some auto parts to prevent rusting. I don't know if it's the best stuff for the job, but for me it was free. I figured it couldn't hurt. I tried not to get any on the brick. I don't know if it would hurt them, but I figured they didn't need it.
I took the chimney cap and fan off, ran a brush down it and plopped a 5gal bucket on top of the stack. I scraped the rear flues also as best I could and coated with same stuff. Just wondering, have you found an "easy" way to scrape the vertical flue towards the middle of the unit? That was the only "pain" I could find with the Wood Doctor.
I closed the door but did not latch it tight. I figured it was better off "breathing" than with temp changes creating sweat inside.
Turned off power. Topped off water (if needed)
Also, if I still had my HE5000, I would be in need of replacing 2 fire brick which were cracked.