I've actually managed to mess with it enough to get it to say the correct Asr time for me. Although I don't know anything about CSS, Java, or HTML, I was able to understand enough to know what parameter needed to be changed: based solely on
praytimes.org and the code provided there, in the calculation for Asr time, a single pre-set parameter is changed to make the correction. This parameter is the 'asrJuristics' for which the value is either "Hanafi" or "Standard"; the latter is the default. This system already exists in the code, all that needs to be done is to provide a way to select one over the other in the options page and have that permeate through the time calculation/presentation. Since I have no idea how to implement it, I literally just went through all the script and HTML files on my computer in the Chrome folder associated with the extension (which I found at C:\Users\[username]\AppData\Local\Google\Chrome\User Data\Default\Extensions\ndmbeogingkjkmmkoomnigifmpajmbkc\3.0.2_0) and searched for "asr" and "Standard" and changed it manually to "Hanafi" i.e. I changed the default to "Hanafi" because it was easy to find where that was set.
I just didn't know where or how to implement it for it to take effect in the options page.