Not sure if I understand cmopletely because you have three names floating around: DBNEW, DBSQL and DBOLD\SQL. How I read the post is that you want requests that were going to named instance DBOLD\SQL to start being served by default instance DBNEW on a different server meaning I will ignore DBSQL as a typo.
You can use port forwarding at the network layer to accomplish the redirection. Or you can configure DBNEW to answer on the same port as DBOLD\SQL instead of on the default port 1433. In the port forwarding scenario I think you'll still need to have the instance name DBOLD\SQL online in some form so the SQL Browser Service can continue to dole out the port # for requesting clients. Most of this is conjecture about how I understand the browser service functions and how I understand it to have been setup in a shop I previously worked in where the config management team did not have a handle on all the code/config-data they managed, note that I have never actually set this up 🙂
IMHO this is a slippery slope and the config management team in the aforementioned shop was fighting the equivalent of spaghetti code in the DNS servers and routers to deal with all the forwarding they had signed up for when in hindsight they knew they should have just done the work up front to change the config files and all clients when a server was migrated...why can't you just have all the client start going to DBNEW?
There are no special teachers of virtue, because virtue is taught by the whole community.
--Plato