If it’s an AA DP then the simple solution is that if you’re going to jump don’t be predictable. I use a mix of lariats, Focus-dash cancel and EX hand (and occasionally non EX) to approach more often than I jump (or at least I’d like to think so) I like focus since it prompts them to do unsafe things like tatsu and will make them throw less fireballs (they’re helping you build ultra) or be more aggressive to make that little piece of grey disappear. This means more pokes or jump-ins and to me that means AA lariat and EX hand becomes a more viable option. It’s not an untechable knock-down but it does leave you right next to them which is where you want to be.
Jumping still works though. Learn the range of J.Fierce (I once joked with a fuerte player that I was missing with it against him because I’m too used to punching shotos in the head with it and nothing else). At the right range you can jump a fireball and smack them in the head during their recovery. At that same range they can’t really use anything to AA you either and if they can it’ll probably be a risky and inconsistent punish.
If you’re in range where DPs will hit then yeah you have to be a bit more reserved since if they’re fighting gief it generally makes people quite nervous. If you block a DP (or in some situations where it will whiff in front of you) You’ll more often than not be able to land a Jab SPD, then green hand in for a mixup. This is on the assumption that it’s a jab DP. Higher strengths generally mean an easier chance to land a bigger punish.
The DP doesn’t really have priority over absolutely everything (I’ve seen Ryu’s trade with gief’s C.LP) but it’s a very good “get the **** off me” move and that is generally how they tend to use it. If you expect it and be patient with them then they’ll eventually give ground and push themselves close to the corner. The other alternative is moving towards gief and if you’re on the ball then they’ll be taking some damage and possibly a knock-down leading to gief wakeup pressure.
Above all: Patience. 99 seconds can be a surprising amount of time and I’m not sure anyone can change the way the match is going faster than gief once he gets momentum.