My chimney... like the stone part with the concrete pad, is a good 3' above the peak of my roof. The terracotta liner extends up another foot, with the grate/raincap thing on top of that. Think I should still leave it hanging sideways?
No, just don't cut it flush with the terracotta for now, you can cut the insulation flush, leave a small hunk of liner beyond that though incase you need to add the class A pipe to make better draft, you'll know after running the stove for 2-3 weeks what your working with, draft is more finicky in warmer temps then cold temps, so if your drawing good with temps in the 40's then you'll do even better when it drops to the 20's & 30's. I just don't want to see you do the same work twice, a little extra with the rain cap down to the plate that goes over the terracotta will look fine for a few weeks, you can always go back up and button things up.
A good test of draft with a new stove is to first establish that you have dry firewood (seasoned to me is like salt and pepper, your little is my a lot) grab a moisture meter from mernards, split open a peice of firewood and test the new face by inserting (kind of firm) the prongs into the split, if your below 20%, your good to go,
Do your break in fires, read your manual first, but essentially you want to bring the stove temp up in incremental steps to cure the paint, during that time your going to smell paint and veg oil burning off both the stove and liner (coated in factory to keep from rusting while in storage)
As you do your break in fires you will start to get a handle on your draft, start ups might be sluggish, but as long as your not flooding the house with smoke while temps are in the 40's you should be good to go, after your 3rd break in is done, make a regular fire, let it get established, the turn the air to half way, after the fire is seated, slowly open the door, if you have good draft you shouldn't have any large puffs of smoke that come inside, if you do consistently get smoke inside the house when you open the door on an established fire, you try adding a 3ft length of cheap black pipe to the end of the chimney liner, if you see an improvement then you know to add the class a pipe. If there is no improvement, try cracking a window open near the insert, this will establish whether your fighting a negative draft issue or not, also make sure when opening the loading door that the bathroom fan, range hood or the dryer isn't, those are big air suckers.