The brown color you are getting may bee from iron discoloration. Having metal ions in your conc. sulfuric acid can give real problems in some reactions. For other uses, it may turn out OK. As far as purifying sulfuric acid, you have to do all that work while it's dilute. After it's concentrated, what you see is what you get.
The charcoal cleaning is also best done at the dilute stage. Float your charcoal in water, and use only the bigger stuff that settles first --- you've got to filter that. Sometimes you may have luck in filtering cold battery acid thru paper, if you do it FAST before it eats the paper. Generally, though, you filter sulfuric acid thru glass.
You used a beaker, I would use a casserole for more exposure to the air. Working always outside, I'd heat it (below boiling) down to ~1/3 volume. My rule of thumb was to heat it until it stopped steaming and started smoking. You can see the difference. 93-95% should serve for most applications, at that strength it will char sugar or paper. To get 98%, you'll need to use a water aspirator. Just heat to get the water out, don't try to raise a boil. Don't sacrifice your vac pump for this. And no, you won't distill sulfuric acid. Just forget that notion.
A beaker down, and a barrel to go? Gives you lots of incentive to get that brown stain out. Assuming it's in your acid source, and not a result of processing. There must bee something, acid insoluble, which can be added to flocculate your impurity out of the 30% acid. Can't think of it right now. You can try Ca(OH)2, to precipitate out calcium sulfate, but I doubt you could hook much of your impurity that way. Good luck anyway.
turning science fact into <<science fiction>>