As far as the federal reserve is concerned, dollar coins can only be ordered in $2000 increments, doesn't matter if they are large or small.
To order Ikes from the fed, the order is placed as a normal order for small dollar coins, but then the order is intercepted at the coin vault where large dollars are substituted. There is usually a special handling fee for this service imposed on the bank.
With Garda and other "high" volume depository institutions, the instructions to substitute the Ikes is often missed and the small dollar coins are shipped out instead. This can cause quite the headache for your bank as they have already been charged the special handling fee and need to call up the DI to get it refunded. DI's like Garda have crappy customer service, so the request for a refund can be a time consuming process.
Not all banks deal directly with the DI's, but rather they deal with smaller cash management services. Others may deal directly with the DI, but not have an account with the federal reserve. Often, the response in these situations is mixed. The company will most likely charge an even higher special handling fee for getting IKE's, but often will waive it if the company has "loose" Ike's on hand (aka an odd amount not equaling $1000) and the bank settles for the loose amount.
Every situation is different but I can tell you this
No coin rolling service rolls the Ike's anymore!
If you find rolled Ikes, they are either hand rolled, or they were rolled some 20 years ago and were never opened.
Good luck and I hope this helped clear a few things up for the OP.