Variable Width Stroke values for Script

holy smokes! yeah I see, it wouldn't work for that kind of file. But even if you could have access to the UI Point Editor data, you file is way to complicated. 

try saving as svg, the width profile is probably expanded at export time.

the simple line I posted above exports as

<?xml version="1.0" encoding="iso-8859-1"?>
<!-- Generator: Adobe Illustrator 24.0.1, SVG Export Plug-In . SVG Version: 6.00 Build 0) -->
<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
width="288px" height="560px" viewBox="0 0 288 560" style="enable-background:new 0 0 288 560;" xml:space="preserve">
<g>
<path d="M28.68,231.53c4.04-2.29,8.09-3.74,12.13-5.01c4.04-1.24,8.09-2.14,12.13-2.81c4.04-0.66,8.09-1.07,12.13-1.28
c4.04-0.24,8.09-0.12,12.13,0.65c4.04,0.72,8.09,2.06,12.13,3.26c4.04,1.23,8.09,2.25,12.13,2.64c4.04,0.41,8.09,0.29,12.13-0.16
c4.04-0.45,8.09-1.38,12.13-2.43c4.04-1.06,8.09-2.19,12.13-2.96c2.02-0.39,4.04-0.71,6.06-0.96l6.06-0.66
c4.04-0.43,8.09-0.88,12.13-1.19c4.04-0.29,8.09-0.41,12.13-0.23c8.09,0.36,16.17,1.48,24.26,3.2c4.04,0.86,8.09,1.9,12.13,3.18
c4.04,1.3,8.09,2.74,12.13,4.76v2.3c-4.04,2.03-8.09,3.46-12.13,4.76c-4.04,1.28-8.09,2.31-12.13,3.18
c-8.09,1.72-16.17,2.84-24.26,3.2c-4.04,0.18-8.09,0.06-12.13-0.23c-4.04-0.31-8.09-0.76-12.13-1.19l-6.06-0.66
c-2.02-0.24-4.04-0.56-6.06-0.96c-4.04-0.76-8.09-1.9-12.13-2.96c-4.04-1.05-8.09-1.99-12.13-2.43c-4.04-0.45-8.09-0.57-12.13-0.16
c-4.04,0.39-8.09,1.41-12.13,2.64c-4.04,1.19-8.09,2.54-12.13,3.26c-4.04,0.77-8.09,0.89-12.13,0.65
c-4.04-0.21-8.09-0.62-12.13-1.28c-4.04-0.67-8.09-1.57-12.13-2.81c-4.04-1.27-8.09-2.73-12.13-5.01V231.53z"/>
</g>
</svg>

not that I know of, maybe if you expand appearance you can read the anchor points. does that help?