But it will have the cost of 2x API bandwidth (vs 0) and another point of failure that you are responsible for. A DNS CNAME probably wouldn't work if you had to go over SSL. Maybe a 30x redirector (still have the SPoF, but simpler and much less bandwidth)? Except in the past, I've found that most clients react poorly to redirects for anything other than GETs.
Is there any indirection that would avoid having to walk the traffic over my own network?