I have some experience with this in the "great-white-hunter" type of tent, and dang!, but it is nice to come back to a tent that you can get to 70-80F quickly. Consider that in Alaska, yeah, we've got cold temps, wind, rain, and snow, but almost more importantly, between Sept 21 and March 21, our days are shorter than yours. 5-8 hours of sunlight plus a few hours of dawn-dusk leaves a lot of dark hours every day so it's much harder to stay warm by staying active outside. Having dry clothes in the morning is also a wonderous thing.
Yes, if your chimney is sealed (even loosely), all the hot gases and sparks will be taken outside. Usually, these tents are canvas and more tolerant of a few sparks. Some background engineering info:
Chimneys can be too short (not enough draft), too narrow (a restriction to flow), too wide (rare, but the heat can be diluted in a big stack and not develop a good draft). A chimney can not be too tall. Taller is always better. You MUST have enough "draft" - negative pressure - inside the stove and chimney to keep hot gases and sparks inside. With good draft, all leaks will leak air INTO the stove/chimney. This is also true during refueling - with good draft, air flow with INTO the refueling door, although obviously a smaller door is better in that regard.
Yes, a wire screen at the outlet will reduce the size of cinders that might get airborne. So too will greater chimney height so cinders are more completely burned when they exit. Also, a taller chimney will give a longer drop time for cinders to cool before possibly landing on the tent.
Ideally, the chimney should be at or above the peak of the ridge line to avoid sparks being caught in a wind-induced eddy.
A few brainstorming ideas:
While your lower stacks of chimney must be steel, you may be able to transition to aluminum for upper sections. Learn to make and break the seams of the ducts and you can nest them inside each other and really save on space.
I'd seriously consider getting stainless for the first section of duct if you will use it a lot. That first section is not only the hottest (duh) but also has the most reactive species in the exhaust gases.
Could you put a "sacrificial" layer on the downwind side of the tent? A thin cotton layer with an air gap to protect the cuben / silnylon below?
You need to leave a awful lot of space around a hot stove to avoid melting clothes, sleeping bags and skin. You'll sleep fewer people inside with the stove fired up. Hence, this works better in large tents than in small.
Test all of this at home first. Cover the cuben/silnylon in old cotton sheets for protection and stretch a painter's 2 mil poly drop clothe over the downwind side to look for potential damage. If there is only one of you, get a free time-lapse app for your phone and set it to record the stack/sparks as you jiggle the stove, start it, refuel it, put trash in, etc.
And, to say it one more time: Whatever the problem, a taller chimney is the first thing to try.