Does that old glitch still work? Oghma and the invisible chest in Dawnstar are still present, so I figure it is within the realm of reason to believe that the glitch still might work.

I think you have to collect whatever ingredients are necessary for a Fortify Alchemy potion, and then loop drink and create those for a while until you're adequately fortified, and then one would make a Fortify Enchanting potion (or two.) Then, the player would be able to make a sword with a 38256729 Fire Damage enchantment, or something similar.

I have Hearthfire and Dawnguard installed. Skyrim itself was redeemed via a code that came with my system, so coming straight from Xbox Live, I assume I have whatever the most recent update is.

There is no fortify alchemy potions. You must craft Fortify Restoration potions (Abecean Longfin/Cyrodilic Spadetail/Salt Pile/Small Antlers/Small Pearl) 2 of them. Look on the page other posts on that. I hope that you don't have mods that glitch the process..

My mistake. I've already started collecting the Fortify Restoration ingredients and the Fortify Enchanting ingredients, and I'm hoping that my efforts aren't fruitless.

I hope too... Don't forget to enchant 5 gears (circlet, Falmer helmet, gloves, necklace and ring). You can wear a circlet together with a Falmer helmet. Good luck.