Success! Got it working here's how it looks.
Sometimes you just have to leave people alone and they will figure stuff out
Now, here's what I'm seeing (red grid lines):
SublimePTY.tmTheme uses white[fg].black[bg] as a default screen color. If console reports any character as white.black I don't have to add any region and: a) everything works faster b) borders are not present.
You've changed console text color to green, because of that each character is reported as green.black (even if it's a [space]) and there are a lot of regions to apply.
Edit: Noticing that it is very slow frame rate as well,
_apply_colors() is slow, I promise I'll try to improve it asap.

I hope you figure out a way to run terminal without having to run cmd prior to starting Sublime.
I know exactly how to enable this, but I also know that once I make it too easy to run SublimePTY, people will start using it for real tasks (against my every advice) and I'll be flooded with requests. As you've probably noticed, it's still an alpha/prototype, lets say running console_server.py is a test

If you create two regions (one solid, one outline) you can probably get rid of the different color border. That won't help the rounded issue at the corners, but it would help it look a bit better.
I had the same idea, but combining any DRAW_EMPTY/DRAW_EMPTY_AS_OVERWRITE with DRAW_OUTLINED (in any order) did not yield anything useful. It seems as if any additional regions are ignored when DRAW_EMPTY or DRAW_EMPTY_AS_OVERWRITE is used.