I also have a Twin and the only Distortion/OD that I have liked for it is a Fulltone OCD .
Yeah, I have an OCD. It was fine into my Twin with the big square magnet CTSs, but like I said, I just came to the conclusion that I don't care for much gain into JBL speakers or the Weber California knockoffs.
I would say that with the right speakers... and there are lots of 'right' speakers... CTS, Utahs, Oxfords, bigger magnet ceramic Jensens and certainly many Celestions... the Direct Drive is incredible for getting Marshall tones. Like I said, we compared a few of Doc Morbius's amps with the Direct Drive and a guitar with 57 Classics and we simply couldn't believe the Marshall tones that were coming out of his Silverface that had the one Utah and one 12F150. The Twin with the Californias... not happening. Sounded holy when clean and loud, but not good at all with gain.