I was referring to a 6 inch insulated liner fitting easily. (That's what I would do) The stoves I tested when adding baffles were actually 15 feet from stove base to chimney top, but it was a 6 inch insulated metal chimney straight up. Many new stove manufacturers instructions require 15 feet from stove base, but that is only due to how they were tested and not what is physically needed to make them work. If you baffle it, that's the minimum you should have.
Depending on how much your pipe is being air cooled, you have next to no chimney. Like putting a 2 cylinder engine in a large vehicle.
If you can put a magnetic pipe thermometer on the inner flue pipe, double the reading for approximate inner flue temperature. Single wall pipe drops drastically as you go up loosing its heat to surrounding air.
I don't know which model Grandma you have, flat top doors had no baffle, but the later Model III had a baffle after 1980. They have arched top doors and no angle iron down the corners and a tag on rear shield. If you have a GM III with glass doors, the doors will be the same as your insert. GM IV will have a larger glass viewing area.
Grandma with solid doors should have a damper in connector pipe as well. There are factors to consider when adjusting the space where exhaust will flow above baffle. Elbows, cap, and screen all add resistance to flow, so that increases the area or smoke space to allow enough heat up for the larger chimney. Consider that chimney large engine that requires a lot of heat to make it work. And yes, that is the reason that stove has much more BTU capability. It would be as efficient as you could get with a 6 inch that high and baffled. With the 8 inch diameter you have twice the area to keep above 250* so a lot more heat is required to be left up. The more heat you can keep in the stove, the more usable heat you have for the house. The Insert will perform the same way with the same chimney, providing you have enough cfm blower. So connecting the Grandma to the flue upstairs would disappoint and have the same lowered heat output as the Insert now. Bottom line, the Insert doesn't get enough air inside it to create the BTU you expect. It needs a hotter flue.
Does the Insert tend to soot up the glass needing daily cleaning? You should be able to get it going by opening primary side intakes along with air wash open slightly, and when the flue is up to temp (that may not be possible with current inner flue) close side draft caps and burn with front air wash open only. Little to no glass cleaning is then required.
You may have a "Brass and Glass" Insert there as well. Can't see the trim on your picture. Many doors have been painted over and cover the brass plating. Lacquer thinner when cold will remove paint to test or ONLY metal polish for precious metals such as brass, gold and silver should be used to remove paint or clean the polished brass. The raised areas around door edge and around glass are the places to test and shown below. Not all are the more expensive Brass and Glass. They were available with black painted glass doors.
Raised areas were machined smooth and entire door was plated, then painted. The raised areas are wiped clean with mineral spirits to remove paint and over spray before final cure with heat. Grandma III with Brass and Glass shown.