Great so thats gonna take forever:)
The only thing that will take much time is leveling Alteration far enough to allow you to cast the spell. Iron ore is incredibly easy to gather in large amounts. The spell tome is a static item, found in 3 separate locations, so it isn't like you would have to wait for it in random loot... The following website lists exactly where to go to find the tome. http://elderscrolls.wikia.com/wiki/Transmute_Mineral_Ore, for those of you who don't want to bother hunting for it...
Also, consider reinvesting some of the gold you make from crafting rings/necklaces into gems, especially diamonds, sapphires, emeralds, and rubies. Making the various gemmed versions of any future rings and necklaces greatly enhances their value, making smithing level much quicker. Assuming you can cast the transmute spell, you could probably gather sufficient iron ore to complete those last 10 levels in about an hour or so of exploring...