Another place to check is the Random Rack at Howard precision. They sell drops from jobs they have run at really good prices. Some alloys are as low as $1 per pound. You just have to look thru what they have to find something you can use. You might end up with a much bigger chunk than you need at less money and have some left for your stock rack. But call them before ordering, shipping can get pricey on big heavy items.
Howard Precision Metals has a variety of random metals in stock and ready to cut your specifications. Call our sales department to lock in your random piece at 800-444-0311.
www.howardprecision.com
If you go from plate I am guessing that about a 3.75 hole saw slug will be close to the starting size you will need. And it will by default have a 1/4" hole on center to start from.
I just remembered that I have a big chunk of brass tube in the basement, Unfortunately it is only 2.75" OD x .9375 ID x 13 long.