I think you have a decent plan except for just feeding them hay. Our pens allow around 1000 sf/hd which is plenty of room with mud only being a problem in spring. 30 head on 3 acres is around 4350 sf/hd. Your pen is plenty big for 30 head.
As for feeding them. I would seriously look into supplementing them with corn/soymeal or whatever is cheap in your area. Corn is still pretty cheap off the farm. Try to buy your grain for market price or a little less right from the farm. In my area it's 20 cents a bushel to have corn hauled to market, if we end up buying corn we pay market price if they haul it to our place, or 10 cents less if we haul it ourselves. Buying all your feed from the feed store is seriously going to hurt any potential profits.
As has been stated, feeder cattle are very high right now, and there are no guarentees that the price will hold until you sell them, but if you can put enough gain on them, the worst I think you would do would be to break even.
On a side note, let us know if you are actually able to buy hay for less than $10/roll. I am guessing that was just the minimum starting bid for the auction and there were no bids. I am guessing the guy selling it, would buy it back himself if it sold for less than $10 even with commission.