it is never a guarantee, but as i see it you are left with only 4 options, where two of the options seems very remote for you…
options:
sniff the url(s) and use rtmpdump
sniff the stream, filter it, save it and rebuild it.
use a screen recorder
nothing of the above. just continue watching it as you have been doing.
I have been using camtasia studio from techsmith for many years, and it can do this. but it’s a little expensive at $~300. but you have camstudio which is free, and a couple of others too, to help you do this.
I suppose I’m going to have to use a screen recorder <sigh> I thought it would be possible to pull the video from the site but it appears that they have almost guaranteed that this can’t be done.
Download Helper is another (via a google search). Whatever tool you use, make sure that you have the permission, rights, etc to download whatever the video is.