Just finished adjusting the armscye on my trench coat

I ran into almost the same underarm problem last winter with a lined wool coat, and moving the shoulder seam was the trick that saved me too. I dropped mine about an inch and a half and also shaved a sliver off the sleeve cap so it would still fit the new armhole. One thing I'd suggest checking before you stitch is to baste the sleeve in and actually swing your arm around, because the tightness only showed up for me once I did full reaching motions, not just standing still in front of the mirror.

Your gradual flare plan sounds smart for the same reason mine failed the other way around. I put gathers all the way from the hip on a heavy twill once and the top half bunched wierd under the belt, plus the hem got so heavy it dragged the whole side seam out of true. Starting the gathers lower and letting the fabric do the work is definatly the calmer approach. For the lining, one small thing that helped me was cutting it a touch shorter than the shell at the hem so the outer fabric could hang free without the lining pulling on it. Made the drape look cleaner in motion. Would love to hear how the gathers behave once you get the whole thing on a body.

I made a trench out of heavy cotton canvas last fall and hit the same underarm squeeze. Instead of moving the shoulder seam, I kept the armhole where the pattern had it and sewed a small gusset into the underarm seam, just a little diamond of leftover lining fabric. It's invisible once your arm is down and it gave me all the reach I needed for driving and hauling groceries. That might be worth a try if the dropped seam starts fighting with your shoulder line later on. On the skirt, I'd be a little cautious with gathers in a heavy fabric. Mine pooled strangely at the hip, and the gathers pressed flat creases into the canvas that never fully steamed back out. I ended up picking them apart and doing a couple of soft pleats near the side seams instead. Pleats collapse when you sit and they release the volume lower down, wich got me closer to the drape I was chasing. If your gathers are alredy behaving in your fabric, carry on, but maybe press a test section before you commit to any topstitching.

Mine took three muslins before the sleeve sat right, so seeing a coherent piece at this stage means you're well ahead of where I was.

That gradual flare rings true. My mother made raincoats for a living back in the 60s and she never touched a circle skirt on anything heavier than shirting. What she did do, and what I'd pass along, was hanging the finished shell on the form for a couple of days before hemming. Coats drop on the bias, especially where your gathers start, and the hem will walk on you if you rush it. I've had a wool swing coat drop nearly half an inch over a weekend. Mark it with thread tacks, not pins, and check again before you cut anything. You'll thank yourself when that hem hangs level a year from now.

One thing I'd flag on the shifted shoulder seam is that the new position puts the seam right where the fabric wants to stretch, so I'd run a strip of stay tape along it before you sew, otherwise it can grow a quarter inch after a season on a hanger. I learned that the fussy way on a coat where the seam ended up drooping past my natural shoulder by the second winter. Also curious how you're planning to keep the gathers even where they start, since with a heavier cloth the stitching rows tend to pull unevenly and I've had better luck easing over a zigzagged cord than trusting two rows of basting.

Those gentle gathers are gonna make your life easier when you hit the back belt, btw. I tried easing fullness into mine with heavier fabric and it turned into a lumpy mess right where the buckle sits. Had to pick it apart twice. If your flare starts low like you're planning, you might dodge that entirely, but I'd pin the belt on before you commit just to see how everything stacks up. Also curious what you're using to baste the gathers, thread type makes a difference when the fabric's got any heft to it.