I've been having a rough time against Shulks lately. His Sword is so long! It knocks away my can, shatters my clay pigeon, and the gunmen do not help since every Shulk I met on FG and elsewhere jump over the gunmen. And shield monado is an ABSOLUTE pain...
That I can help with. I used to absolutely HATE shulk (he's been replaced with Ike, Sonic and Sheik in terms of my 'absolutely hate' list), then I found his weakness.
Firstly, you need to drop classic DHD projectile usage. As you correctly observe, his sword interrupts projectiles (especially that irritating neutral air 360 spin spam). Your main reliance is roll dodging and baiting - you want to bait his 'back' slash and aerial jumps. Shulk is a very 'forward' heavy character (excepting some moves) and once you realise his back is exposed, he becomes a walk in the park.
Roll dodge 'back' slash, punish with frisbee, follow up with dash attack, air jab. If he's a heavy counter spammer, use can (the can bypasses the counter for some reason and the explosion interrupts him, free pass to attack). Once he's airborne, you want to target his feet with the can (don't go for his front - his feet are his sword's blind spot), but keep sharp for a reactive rapid roll in-case he deflects the can with neutral air. If he attacks at the can prematurely and you see an opening, go for an fair.
Keep on his tail once you juggle, if you're fast enough you'll interrupt his sword strikes before they have a chance to attack. If he's a heavy jump to back air spammer, you want to sit and bait his attack, then roll dodge at the last second (you can then either light rapid jab, frisbee or smash A depending on timing).
You'll want to keep him spaced. Avoid getting trapped on the edge. Jump over him if you have to.
To KO shulk, treat him like you would a little mac but with a higher up jump - bair or can him out of range (can is advised as bair can be overridden by the sword's length).
His disadvantages when using the different modes are as follows:
No art: No weakness.
Smash: he's easier to launch.
Buster: takes more damage, appears easier to launch(?).
Shield: moves slower, sword is shorter.
Jump: jumps higher but loses finese of control, reduction on damage.
Speed: shorter sword, slightly less damage.
Exploit each as you would as if dealing with a character of that class:
Smash: roll dodge, smash As, bairs and any other smash moves.
Buster: frisbee chip damage and opportuntistic launch attempts.
Shield: Outrun, roll dodge, frisbee chip damage, harass.
Jump: Bait/provoke, roll dodge and exploit opening, can to suppress the air.
Speed: roll dodge very actively and light rapid jabs/light attacks on opening, frisbee chip damage.
Once you figure his weakness for each state, he becomes vulnerable. Most will try to switch to jump when recovering (free pass to mid-air intercept), shield when heavily damaged (apply technique regardless until it runs out), and smash when you're high percent. Jump, speed or buster depends on their attack preferences: jump = jump spammer, speed = speedster, buster = aggressive.
Remember, if you can't handle a particular art, just waste his time for about 10 seconds, when it will run out and take another 10 seconds to recharge - that's your opening.
Additional tip: don't be afraid of his sword. If you see him trying to select an art, immediately harass him so he lands on the 'wrong' one, which will totally throw his game. Use anything to force him to do something - anything - to break the art selection (frisbee, can, gunman, dash). Even if he injures you, it means you've thrown his game. If you're a very clever person, you can even force him to break at the art that you want...
He'll spend the rest of the match trying to 'sort out' his art selection, of which you can harass him again, usually for free damage...