...it is my understanding that when you cut a coil off a spring you make it stiffer.
Yes and no. The shorter one will be stiffer (relative to the amount of travel/compression) but in this case the spring is contained in a set amount of space so shortening it creates less preload so less force applied.
...it is not my intention to gain a reputation for being contrary...
Many of us here have contrary tendencies so you should fit right in

Bill