"For movies and music what would be the ideal size and tune for the stereo intergrity's 18 ht-4 for a ported sono ? My dedicated room is 23 x 36 x 12"
that is a personal preference. there is no right answer. below is max spl of the proposed sub (thin green) and one that is 13 cubic feet tuned to 15hz (thick green). more extension means a little less headroom slightly higher up.
" a big contributor in the DIY sub world has this in mind, 72 inch tall, 26 inch round sonotube with an 8 inch X 40 inch Port gets you 11 hz tuned."
that is about 20 cubic feet net. 8x41 port gets you ~12hz tuning, so you are right on, if that is what you want.
you'll have to be careful with power, as only 500 watts or so will push the driver to near its xmax. much more than 1000 and you may start to get into the red zone.