You could always reroute (forward) localhost:2222 localhost:22 using iptables, eg.
iptables -t nat -A PREROUTING -p tcp --dport 2222 -j REDIRECT --to-port 22
See alias port / port forwarding to another local port or this Google search. This, in addition to ControlMaster auto, should not require any additional passwords (either local or remote).
However to me this seems unnecessary and makes me wonder if you don't have a case of the XY problem.