Just nit picking but your Avatar subs are the wrong color, they should be yellow. What you need to do is in BDSup2Sub under the settings menu select 'Swap Cr/Cb', this will make them look wrong in BDSup2Sub but correct once encoded in Handbrake.
Also the frame you have posted seems to be a lossless 1.6meg PNG file but it looks horriblely compressed and soft, what Handbrake settings did you use? and what bitrate did the file turn out to be?
I've said it before I always use a deblocking setting of -1,-1 in Handbrake because I think Handbrake creates encodes that are far to soft and blurry.
It's just a screengrab from VLC. From my experience, when taking a quick screengrab in VLC, quality is never indicative of how good the video actually looks.
I just use the Universal setting. The quality is superb on my HDTV. I don't worry about fine-tuning the settings, I'm perfectly happy with the preset. Bitrate is a little over 5,188Kbps.
As for the subs being the wrong color, thanks for the info.
*I tried your info regarding subtitles. Used BDSup2Sub, clicked on the option you told me... forced subs are still blue.