Well then, you should have more than enough power for your CPU to render Flash unless your CPU is loaded to the max with background programs.
See, what happens is this: when you disable Hardware Acceleration, you are telling Flash to send the data to be rendered to the CPU instead of the GPU. Although CPU rendering is much slower than GPU rendering, this shouldn't affect video resolution that much other than slightly slower buffering. As I stated before, I'm having the same crashes and freezes you are having; however, I've stopped them from happening by disabling Hardware Acceleration.
However, my Flash videos seem to work fine. I can watch YouTube videos in 1080p just fine. The only time I really notice degraded performance is when I'm playing Flash games. Yet you claim the videos are choppy and blurry.
I can explain the blurry. What is happening is the websites you are visiting are downgrading the resolution to 144p (not 1444p, but 144p which is the lowest resolution Flash supports). Why they are doing this, I don't know. Have you tried clearing your cookies and cache? (NOTE: this will log you out of all websites you are logged into).
I don't understand why the videos are choppy. If you have 60MB/s internet, then you have more than enough speed to quickly buffer a video. Especially if the websites are downgrading the quality to 144p.
The only thing I can suggest from here is visit Intel's website and see if they released a newer version of your graphics driver. Try installing that and see if that stops the crashes:
NOTE: Make sure you download the correct drivers. Intel has scores of different display adapters, and they're all labeled "Intel HD Graphics". Make sure you only download and install drivers that are compatible with your specific display adapter.