I'm still working on the DS matchup, I think it's like 5-5. The big thing I found is if he catches you in the air with an air gun you get pushed right back to full screen, where he wants you. You have to slowly creep up with dashes. I believe you can dash in between high guns, but be careful about dashing in after he does low guns, as low guns then high guns will catch dashers.
When you get to about mid screen, try to predict when he's going to throw out one of his ground guns. It's a risk, but you have to jump over the gun and then do an air mace MB to get on him.
From there, do your best not to let him get away... he's probably going to start back dashing like crazy... you can either try to catch him with a MC on his back dash or WE3 to catch up to him. Try to bait out the sword flip.
Now the sword flip deserves it's own paragraph... if you are ducking I've noticed that sometimes he crosses you up and you will be hit by it even if you're ducking (believe me on this one.. the move is not an overhead but if you're ducking at close enough ranges it becomes an overhead). Duck blocking it gives you less push back tho (mid screen), so try to duck the initial hit and then switch to standing block. It's -21 on block I believe so my go to punish combo is 123, f3, 123xxMC (MB will whiff, don't bother) That does 30%. Alternatively, you can do 123, F3, D3 to do an untechable knockdown and keep him close to you, which is probably more beneficial. If you know he's too far away just go for f11xxxWE3, it's like 17% but it's the best you can get.
Once you're in, go to to town... WE3, instant d3's, b22, b23, 22xxWE3... I like to mix those all in, but be mindful of the panic sword flip. If you can bait it tho you get another 30% or 24% untechable knockdown. Good luck.
PS. I would really like to find a good GL on this site to practice against... Lantern's might (his grab) own's WE pressure