I think I can walk into the mint and place an order in person at the bullion counter - haven't been for a while but last time I was there I was able to place an order and pay and lock in current spot price. Delivery was estimated at 6 weeks+ I haven't been for a while so this may have changed. Back on topic - I think there will be more tigers around than rabbits but the price may not reflect this.
Getting back to the Rabbit, I doubt you could get one for under $300 unless you luckily pick one up from someone who doesnt know their true worth.
