I chose 150 ppi arbitrarily, simply because 240 ppi or 300 ppi would have made the image minuscule at the pixel dimensions originally cited.
Bottom line - what size, physically, do you want the print to be? With very long and narrow panoramic prints, there are factors that make printing a trade off. Are you going to frame this? If so, what are you going to do - try to find a stock frame, or have a custom frame made? Because the image is very wide compared to height, at some point the height of the image will be so physically small that height will probably drive the choice of dimensions. So, let's say you want your image to end up being 8 inches tall:
for an 8 inch tall image at 300 ppi, you need 2400 pixels in the image height dimension. Currently, according to your post, your original does not have the necessary pixel dimension (you stated that your original is 18,100 px wide by 1056 px tall). If you choose a print resolution of 300 ppi, then the maximum height your print can be, without adding pixels artificially is 3.5 inches. if you print your current original at 300 ppi, your panorama will be:
60 inches (5 feet!) wide by 3.5 inches tall.
Is this what you were envisioning? Very wide and not very tall. At 240 ppi, you would get something like:
75 inches wide by 4.4 inches tall. In your case, the aspect ratio of your image is like 17 to 1, so your attempt to make the image taller will necessarily make it really wide, and attempting to make it narrower will necessarily make it really short, regardless of what final physical size and resolution your print.
That being said, you need to contact the lab that will ultimately print your image and have them specify the requirements for the final print size. I have had a 20 foot wide by 8 foot tall equirectangular panorama dye-sub printed on fabric from an original that was 14kpx wide (the aspect ratio of an equirect. pano is 2:1, so that the top and bottom was cropped). I had to upres the image for the printer, but the combination of the printer resolution and the viewing conditions worked out well, even at very close viewing distance. So, work with the lab and see what they require.