On defense, your goal isn't to shut down all options , because that's impossible against a good offense. Rather, your goal is to dictate to the offense those options it can take. So, the first thing to realize here is: if Big Thrower hasn't been able to make big throws, you've done something successful.
The question to ask yourself now: Is Big Thrower hurting us more now as a deep receiver than he/she usually does as a thrower?
A few successful deep goals shouldn't automatically make you change your tactics. If, for example, you've also gotten a few turnovers on the other team's handlers because they aren't used to running their handler set without Big Thrower, then maybe those turnovers offset the damage of Big Thrower running deep. I.e., maybe having Big Thrower go deep is a good tradeoff, given the other disruptions it's causing to their offense.
But then let's assume that their offense is running pretty smoothly, or that the errors in their offense have little to do with the way you're covering Big Thrower. In that case, the most important thing is to keep Big Thrower off balance. Even great throwers have a hard time switching from a deep receiver mentality to a deep thrower mentality mid-game — so force Big Thrower to (try to) make that switch, and make the switch as hard as possible. A few ways to do this:
A. Defend Big Thrower by preventing him from going deep — physically prevent him: defender should keep keep his body between Big Thrower and the endzone.
B. If the defender commits himself to superior positioning, then speed and quickness are probably more important here than height.
C. Defender should be an excellent marker. Stay close enough to Big Thrower so that you can put a mark on him as soon as he catches it. Don't go for a layout D on an in-cut unless you're reasonably sure you can get it.
D. A vast majority of the best hucks are released in flow, before stall three. So put a "no huck"/flat mark on Big Thrower for stalls one and two. (Most throwers, especially huckers, don't look to break the mark until stall 3, anyway.) To do this, marker should focus on mirroring his shoulders with the thrower's shoulders, staying on toes, eyes on thrower's chest, arms wide.
Being a great player, Big Thrower is going to get the disc, and is probably going to get off a couple of good hucks. So: measure your defensive success here not by asking "did you shut him down?" but by asking "did you successfully dictate his options?" Specifically, two questions:
1. Did you prevent him from getting open deep?
2. Did you prevent him from hucking on stall 1-2?
If yes, then you've done as well as you're going to do. At least in the context of a person-to-person defense. Zone/junk defense options are also worth considering, but that's a different story.