Hi DaemonUmbra, thank you for taking a look at my problem!
I think I did change the Java Arguments from 2G to 3G (please see attached screenshot 9). But according to my memory, at least one of my previous tries, I did not change the arguments but still got the same thing happening to me. Other than that I don't recall changing anything else.
I have tried again, selected "forge" and hit play and still no twilight forest showing under mod (please see attached screenshot 7, 8, 11).
So what do you think?
P.S. I have also attached the log after my latest try.
debug.log
latest.log