Okay, you don't have a spacer. But that's a very common axle type, so it should be easy to find a replacement cone that doesn't have the cylindrical extension on it. Also, it looks like there's a 1mm washer between the cone and locknut, which you could lose. I've also seen thinner locknuts. You can probably get away with a cone only 2mm narrower if you lose the washer, leaving you 1mm oversize, NBD.

But if you go this way you'll need to re-lace the hub into an off-centre rim (or maybe remove half the NDS spokes; it's a 32h so you'd have a triplet-laced 24h. Not sure if doubling the NDS tension like this would do the job though).

If you're under 65kg or so, you could use a light (400g) Velocity Aerohead OC, and from what I can see of your rim you'd probably be able to re-use your spokes. If you're heavier, Velocity has a couple of beefier OC models around the same ERD (the dimension relevant to your spoke length), or there are a few other companies with OC rims too.

Looks like you mash big gears instead of spinning - this is inefficient, and hard on you and your drivetrain. Try concentrating on your pedal stroke for a couple of months, working to train your muscles to smoothly apply power through ~250° and unweight your legs on the upstroke, and work towards being able to apply that at least around 80rpm, so that it feels like your feet are just floating in circles on the pedals. When you achieve this state of cycling grace, you hardly ever run out of legs; rather, the problem becomes getting oxygen into them quick enough, and this is how you gain cardiovascular fitness.

So if you're not spinning like a pro (big guys push bigger gears slower, but most everyone's sweet spot is between 80 and 100rpm), I'd advise getting that down before upgrading your drivetrain. Unless you're spinning, you don't have much clue what ratios are best for your needs.