The console looks as it's supposed to, if your smithing skill is 43.
Try to go to Alvor's House in Riverwood. There's two potions in the basemant that should give +20% to smithing.
Drink one and see if it makes a difference when you try to improve your stuff. Then try with and without the piece of gear equipped.
If that doesn't make any difference, then I'm out of ideas

I already tried using a potion and it worked. Tried it again just now, still worked.
It's just a guess, but it may have to do with your level in smithing. It could be that your smithing level or perks don't let you upgrade beyond exquisite, and that even with the +smithing item, your level still isn't high enough to get to flawless.
I set the skill to 100 and here are the results:
59 > 102 (legendary) with item
59 > 96 (legendary) without item
skill 50:
59 > 83 (flawless) with item
59 > 77 (exquisite) without item
skill 49:
59 > 77 (exquisite) with item
59 > 77 (exquisite) without item
WTF? 30% potions work, but 20% enchants don't work. What kind of wicked logic it this??! Damn you Bethesda!! You wasted hours of my life!
Crafting in Skyrim is WAY too intransparent! Without internet guides and cheats it's nearly impossible to see through everything!
Could be. Did you and Sheijan make the character with the issue after patch 1.02?
I've made, improved and enchanted daedric and dragonscale gear today without any issues, but I made that character on the release build.
I made the character on 27th, I have no idea when the patch was released. It was my first one.
It starts to go on my nerves. I wasted the whole evening trying to figure out what's wrong. I shouldn't have started crafting at all ;p
But I guess the problem is solved now..
Golden rule: max out every profession before trying to understand anything!
Thank you all for your help.