Show HTML view alongside context menu?

I would love to be able to do this:

...but no matter how I do it, something will not work.

The longer explanation: I'm using a Wacom pen to reduce strain on my wrists, which makes keyboard shortcuts hard to reach. Therefore, I would like to fire whatever default context menu the system or current app offers, but with an extra set of actions next to it.

I have found no way to reliably fire both at the same time. Whether firing the right click from within the HTML menu, as a single action, or as a separate action before or after the show floating HTML action, different problems occur.
Either the HTML menu will take focus and immediately close the context menu (inconsistently so, it may or may not work at times) or the context menu will take focus so that the HTML is unclickable.
A third result may also be that one of the two doesn't appear at all, especially the context menu (and especially in some third party apps that don't seem to like the BTT right click at all. All office apps seem to completely disregard a right click from within BTT.)
In all fairness, Safari will almost always allow me to get what I want. Which is where the screenshot above was made.

Short version: Is there a way to achieve this consistently?