I'm agree with you. I think for some match-up, Secret garden is very good and for this match-up, it's extremely better than disc.Faust cannot mash anything, reversal, throw you without taking any risk and even if he escape from the air, his airdash is very bad. So he will just stay in the corner and you can try to AA him with jK or you can just jump-IB-throw.
Now look at the disc setup during the last round of EVO between Woshige and Nage. You can see the setup weaknesses when you have a good Faust who do smart stuff to escape. You have: IB-throw, IB-2P, 6P, 2P (if you do nothing or backdash) and of course, blitz and super.
In the corner if you don't want any problem with disc, you need to time your disc and your move correctly. For TK Badmoon, you need to delay disc and meaty TK Badmoon. For haircar, you do disc asap and meaty haircar or you delay disc and delay haircar. So that way, the haircar blockstun will increase Faust sprite and the disc will touch.