No other known way, except for other types of Copy-Paste. There is not an "Add Picture" button for the Handouts text box interface, like the one ^^^ there IS when you're posting to this forum. You can do what you said (post the pic to Roll20 forums, then copy it from here & paste into Handout text area). You can also do that from (some) other websites. Select-highlight the part of a webpage that has a pic, COPY, go into handout text, PASTE. Might not work or might be blocked from some sites. Not sure if we can right-cick COPY the pic itself NOT from a webpage, and paste the pic itself (such as from your desktop, computer OS).
