Long Excursion/strong surround is one method of rapidly moving enough air for low frequencies, .i.e. the iron law: low frequencies: move more air. clever vents, ports, passive diffusers: all combine to move more air.
my big 15" velodyne sub had soft foam surround, more surface, less excursion, less powerful amp. My Infinity sub, 10" driver controlled by 1000 watt amp is strong rubber surround, high excursion.
my vintage 15" woofers have pleated cloth surrounds, controlled by monster magnet, woofer weighs 37 lbs each.
speed, (both in and out), needs to be controlled by powerful magnet combined with the material the surround is made of.
Is the maker still around? You can ask Madisound/Parts Express for their knowledge.
btw, you are mentioning cone excursion. the amp/signal will move the woofer cone the same no matter the size of the space, or room's acoustic properties. Those will effect what/how the long throw driver's output reach your ears.