I believe you are correct. 

I would print out the information from Hart and Cooley,
including the installation instructions. With this in hand, I would confer 
- if it's still there -  I can't find it on Google -
with the sheet metal store where I originally bought the chimney cap.

I went to this store driving to Dorchester: 
Interstate 93 South, to the Columbia Road exit,
west on Columbia Road to Mass Ave, 
then north on Mass Ave, where the store is (was) located on the right hand (east side) of
Massachusetts Avenue in Dorchester between Dorchester Brewing Co. and Benny Arnold Car Trading

alternatively, I would try:

Metal Supermarkets Boston (North) is your one-stop-shop for metal. Conveniently located near the intersection of I93 and I95 in Woburn, MA.
Boston (North) | Metal Supermarkets - Steel, Aluminum, Stainless, Hot ...
https://www.metalsupermarkets.com

or

Boston Mechanical Engineering HVAC Sheet Metal | Cannistraro
cannistraro.com/what-we-do/sheet-metal/
Cannistraro, located in Watertown MA offers mechanical engineering, sheet metal contractors and fabricators for HVAC air systems.

and, having familiarized myself with Hart and Cooleys Installation Instructions,
ask them a) for advice, and b) to sell me the fittings necessary to extend the metal chimney from the roof into the basement.