IC improves with longer focal lengths (in any given lens design, all else being equal), smaller f/stops, and when focused at closer distances than infinity.
Huge image circles perhaps matter most with rise & fall, such as when trying to fit a building, tall tree or nearby mountain peak into the frame, or to place the horizon at the top of the frame (or people's feet at the bottom) while keeping the camera level (levelled to keep converging lines and perspective under control). Tilting and swinging rarely uses up a huge image circle. If you have a camera with back tilts and swings you can coax a bit more out of a lens with a tight image circle and the swings and tilts occurs within the cone (e.g. it can correct for tilting the camera up or down, etc).
I have a lens capable of "moving" a subject/horizon line in a portrait orientation from the top to the bottom of the frame using rise/fall. It has a 301mm image circle at f/22 at infinity focus. It's a bit longer than you specified, a 210mm Caltar IIN (same as Rodenstock APO Sironar N) a common enough Plasmat type lens that can be found used nowadays for ~$200 USD or even a little less. Another suberb under $300 lens with a good sized image circle would be the classic Ektar 203mm f/7.7.