Chrome for iOS is essentially just Safari for iOS with a different user interface. Apple don't allow any other browser rendering engine other than the built-in webkit rendering engine to be added to iOS.
You didn't find a definitive answer in your search because this isn't really any one single solution - other than to amend Moodle to open the course in way that doesn't use iframes. That's what Totara (enterprise version of Moodle) does - it's called New Window (Simple) and works very well.There's some discussion around how that can be done here.
Unfortunately iOS-Safari's handling of iframes is just really poor, some of the problems with it are listed in this post (that whole thread is worth reading btw). Last time I checked there were 741 open issues mentioning 'iframe' on webkit.org - some have been kicking around since 2006 :-(
AFAIK it has been a problem since Moodle 2...